Matematisk institutt
http://hdl.handle.net/10852/5
Mon, 20 Aug 2018 12:37:59 GMT
20180820T12:37:59Z

A MalliavinSkorohod calculus in L^0 and L^1 for additive and Volterratype processes
http://hdl.handle.net/10852/62990
A MalliavinSkorohod calculus in L^0 and L^1 for additive and Volterratype processes
Di Nunno, Giulia; Vives, Josep
In this paper we develop a Malliavin–Skorohod type calculus for additive processes in the L1 and L1 settings, extending the probabilistic interpretation of the Malliavin–Skorohod operators to this context. We prove calculus rules and obtain a generalization of the Clark–Hausmann–Ocone formula for random variables in L1. Our theory is then applied to extend the stochastic integration with respect to volatility modulated Lévydriven Volterra processes recently introduced in the literature. Our work yields to substantially weaker conditions that permit to cover integration with respect to e.g. Volterra processes driven by alfastable processes with alfa < 2. The presentation focuses on jump type processes.
© 2016 Taylor & Francis
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/62990
20170101T00:00:00Z

Fullydynamic riskindifference prices and nogooddeal bounds
http://hdl.handle.net/10852/62989
Fullydynamic riskindifference prices and nogooddeal bounds
BionNadal, Jocelyne; Di Nunno, Giulia
The seller’s riskindifference price evaluation is studied. We propose a dynamic riskindifference pricing criteria derived from a fully dynamic family of risk measures on the L_pspaces for p ∈ [1, ∞]. The concept of fullydynamic risk measures extends the one of dynamic risk measures by adding the actual possibility of changing the risk perspectives over time. The family is then characterised by a double time index. Our framework fits well the study of both short and long term investments. In this dynamic framework we analyse whether the riskindifference pricing criterion actually provides a proper convex price system, for which timeconsistency is guaranteed. It turns out that the analysis is quite delicate and necessitates an adequate setting. This entails the use of capacities and an extension of the whole price system to the Banach spaces derived by the capacity seminorms. Furthermore, we consider the relationship of the fullydynamic risk indifference price with nogooddeal bounds. Recall that nogooddeal pricing guarantees that not only arbitrage opportunities are excluded, but also all deals that are “too good to be true”. We shall provide necessary and sufficient conditions on the fullydynamic risk measures so that the corresponding riskindifference prices satisfy the nogood deal bounds. The use of nogooddeal bounds also provides a method to select the risk measures and then construct a proper fullydynamic riskindifference price system in the L_2spaces.
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/62989
20170101T00:00:00Z

CR extensions with a classical Several Complex Variables point of view
http://hdl.handle.net/10852/62486
CR extensions with a classical Several Complex Variables point of view
Sonne, August Peter Brådalen
Mon, 01 Jan 2018 00:00:00 GMT
http://hdl.handle.net/10852/62486
20180101T00:00:00Z

Xray PTV Measurements of Solitary Waves
http://hdl.handle.net/10852/62384
Xray PTV Measurements of Solitary Waves
Smith, Lisa; Hu, Bin; Kolaas, Jostein; Jensen, Atle; Sveen, Johan Kristian
The aim of this study is to measure velocity fields and accurate surface elevation in solitary waves utilizing a fast Xray PTV system. It is difficult to measure the free surface of water waves with the optical measurement techniques available today. This is partly due to refraction and reflection of light rays by the surface of the waves, or by reflections of light rays by the wall of the wave tank. The interface between water and air will then get an inaccurate location in images captured by visual light. The use of microelectronics in image sensors, have made it possible to capture images with both high spatial and temporal resolution. In this study, Xray measurements with high resolution in space and time have been performed on solitary waves. Two perpendicular Xray systems are utilized. Surface elevation measurements with accuracy of 0.12 mm are presented, and crosswaves due to wall effects are observed when the average wave height is subtracted from the images. Particles that absorb Xray are seeded into the water and PTV is used to find velocities in the flow field. The two Xray systems provided enough information to produce a 3D reconstruction of the flow field. The velocities measured are compared to velocities computed by a Boundary Integral Model (BIM). There seems to be discrepancy between the computed and the measured velocities, which may be linked to inaccuracy in the particle’s location or linked to the large size of the particles.
Fri, 01 Jan 2016 00:00:00 GMT
http://hdl.handle.net/10852/62384
20160101T00:00:00Z

Large eddy simulations of a buoyant plume above a heated horizontal cylinder at intermediate Rayleigh numbers
http://hdl.handle.net/10852/62383
Large eddy simulations of a buoyant plume above a heated horizontal cylinder at intermediate Rayleigh numbers
Grafsrønningen, Stig; Jensen, Atle
Large eddy simulations of a buoyant plume forming above a heated horizontal cylinder with a Rayleigh number of 9.4E7 is carried out and compared with experimental data. Natural convection heat transfer from a horizontal cylinder at this intermediate Rayleigh number involve a laminar to turbulent transition downstream the cylinder. A laminar to turbulent transition will alter the flow characteristic downstream cylinder considerably, thus it is important that the transition is captured in the simulations. Subgrid stresses are accounted for using the dynamic Smagorinsky model which allow for both laminar and turbulent flow through the dynamic procedure.
The results show a considerable difference between the numerical and experimental results. Plume center vertical velocity is highly overpredicted compared to the experimental data. The computed halfwidth about 1.5 y/D downstream the cylinder is comparable to the experimental data, however, 3.5 y/D downstream cylinder, the halfwidth is only about half that of the experimental data. The halfwidth growth rate measured in the experiments remain higher than the computed growth rate throughout the domain of interest.
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/62383
20170101T00:00:00Z

Detailed measurements of interfacial dynamics in airwater pipe flow
http://hdl.handle.net/10852/62382
Detailed measurements of interfacial dynamics in airwater pipe flow
Ayati, Anis Awal; Vollestad, Petter; Jensen, Atle
Stratified airwater flow in a horizontal pipe is investigated experimentally using particle image velocimetry and conductance probes. This flow regime is characterized by a complex interplay between a turbulent airflow and propagating waves at the interface. The waves are generated by interfacial shear and pressure forces exerted by the faster flowing airflow. The goal of this study is to characterize the waves by means of statistical and spectral methods, and to explore the influence of different wave regimes on the airflow.
Two cases in which the air bulk velocity increases from 2.4 m/s (case A) to 3.5 m/s (case B), while the liquid velocity remains constant at 0.26 m/s, are assessed in detail. Case A belongs to a region of flow conditions in which wave amplitudes grow as a consequence of increasing gas flow rates, i.e., wave growth regime. Meanwhile, case B is in a regime of saturated wave amplitudes. In the first case, the interface was populated by small amplitude 2D waves of relatively small steepness (ak ≈ 0.07). These waves obey Gaussian statistics and are thus considered to be linear. In the second case, the waves are larger, steeper (ak ≈ 0.13) and considerably more irregular. They display nonlinear behaviour (steep crests and long troughs) and their exceedance probability distribution deviates significantly from Gaussian statistics. Bicoherence maps show evidence of both overtone and subharmonic interactions.
Airflow velocity fields acquired by PIV were subjected to a conditional phaseaveraging method based on a steepness criterion. The phaseaveraged vorticity field shows evidence of shearlayer separation above the steeper waves of case B. Hence, in addition to nonlinear mode interactions and microbreaking, shearlayer separation may contribute to the transition from the growth regime to the saturation regime.
Mon, 01 Jan 2018 00:00:00 GMT
http://hdl.handle.net/10852/62382
20180101T00:00:00Z

Consistency between sea surface reconstructions from nautical Xband radar Doppler and amplitude measurements
http://hdl.handle.net/10852/62381
Consistency between sea surface reconstructions from nautical Xband radar Doppler and amplitude measurements
StøleHentschel, Susanne; Seemann, Jörg; Nieto Borge, Jose Carlos; Trulsen, Karsten
This study comprises the analysis and the interpretation of the coherent and the noncoherent parts of a coherentonreceive microwave radar at grazing incidence conditions. The Doppler measurement is an extension of standard civil marine radar technology. While intensity images require interpretation based on understanding the underlying imaging mechanism, the Doppler signal measures the motion of an area of sea surface and is therefore closely related to the wave physics. Both the measured Doppler signal and the backscatter intensity signal are suitable for surface inversion and give almost identical surface elevations. A statistical comparison with a nearby buoy showed good correlation for the significant wave height and the peak period. By comparing the Doppler signal and the amplitude in the backscatter, the study amends the understanding of imaging mechanisms in marine radars at grazing incidence.
This research was originally published in Journal of Atmospheric and Oceanic Technology. © 2018 American Meteorological Society
Mon, 01 Jan 2018 00:00:00 GMT
http://hdl.handle.net/10852/62381
20180101T00:00:00Z

Bimodality of Directional Distributions in Ocean Wave Spectra: A Comparison of DataAdaptive Estimation Techniques
http://hdl.handle.net/10852/62380
Bimodality of Directional Distributions in Ocean Wave Spectra: A Comparison of DataAdaptive Estimation Techniques
Simanesew, Abushet; Krogstad, Harald E; Trulsen, Karsten; Nieto Borge, Jose Carlos
The properties of directional distributions in ocean wave spectra are studied, with an emphasis on sea states with bimodal directional distributions in the highfrequency tails of singlepeaked wave systems. A peaksplitting tendency has been a challenge in the interpretation of results from some dataadaptive estimation methods. After a survey of the theory, mathematical and numerical explanations are presented regarding domains of uni and bimodality for symmetric Burg and Shannon maximum entropy methods. The study finds that both the Burg and Shannon maximum entropy methods have a tendency to split peaks, and that the domains of uni and bimodality for these two methods depend on the Fourier coefficients input into the algorithms. Comparisons of dataadaptive methods based on data collected near the Ekofisk oil field in the North Sea and from nonlinear wave simulations are presented. The maximum likelihood (ML) method, the iterative maximum likelihood (IML) method, and the Burg and Shannon maximum entropy methods are applied. A large fraction of the directional wave spectra from Ekofisk shows bimodal features for distributions above the spectral peak for all of the abovementioned methods. In particular, strong similarity in bimodal features between the iterative maximum likelihood and the Burg maximum entropy methods are found. In general, the bimodality is consistent with previous observations, and it seems to be associated with wave and spectral development owing to nonlinear wave–wave interactions rather than being associated with the peaksplitting tendency in the estimates from any of the algorithms. The bimodal directional distributions were sometimes persistent and sometimes formed or decayed within the order of hours.
This research was originally published in Journal of Atmospheric and Oceanic Technology. © 2018 American Meteorological Society
Mon, 01 Jan 2018 00:00:00 GMT
http://hdl.handle.net/10852/62380
20180101T00:00:00Z

Extreme wave statistics of counterpropagating, irregular, longcrested sea states
http://hdl.handle.net/10852/62379
Extreme wave statistics of counterpropagating, irregular, longcrested sea states
StøleHentschel, Susanne; Trulsen, Karsten; Rye, Lisa Bæverfjord; Raustøl, Anne
Extreme wave statistics of unidirectional and counterpropagating seas are investigated, for the special case of longcrested irregular waves, with laboratory experiments and with numerical simulations using the higher order spectral method. Both the kurtosis of the surface elevation and the exceedance probability of the crest height are larger in unidirectional seas than in counterpropagating seas. Numerical simulations show that even a small amount of wave energy travelling against an essentially unidirectional wave system can significantly reduce the kurtosis of the surface elevation.
This research was originally published in Physics of Fluids. © 2018 AIP Publishing
Mon, 01 Jan 2018 00:00:00 GMT
http://hdl.handle.net/10852/62379
20180101T00:00:00Z

Measurement of the dispersion relation for random surface gravity waves
http://hdl.handle.net/10852/62377
Measurement of the dispersion relation for random surface gravity waves
Taklo, Tore Magnus Arnesen; Trulsen, Karsten; Gramstad, Odin; Krogstad, Harald E; Jensen, Atle
We report laboratory experiments and numerical simulations of the Zakharov equation, designed to have sufficient resolution in space and time to measure the dispersion relation for random surface gravity waves. The experiments and simulations are carried out for a JONSWAP spectrum and Gaussian spectra of various bandwidths on deep water. It is found that the measured dispersion relation deviates from the linear dispersion relation above the spectral peak when the bandwidth is sufficiently narrow.
Thu, 01 Jan 2015 00:00:00 GMT
http://hdl.handle.net/10852/62377
20150101T00:00:00Z

On dispersion of directional surface gravity waves
http://hdl.handle.net/10852/62376
On dispersion of directional surface gravity waves
Taklo, Tore Magnus Arnesen; Trulsen, Karsten; Krogstad, Harald E; Nieto Borge, Jose Carlos
Using a nonlinear evolution equation we examine the dependence of the dispersion of directional surface gravity waves on the Benjamin–Feir index (BFI) and crest length. A parameter for describing the deviation between the dispersion of simulated waves and the theoretical linear dispersion relation is proposed. We find that for short crests the magnitude of the deviation parameter is low while for long crests the magnitude is high and depends on the BFI. In the present paper we also consider laboratory data of directional waves from the Marine Research Institute of the Netherlands (MARIN). The MARIN data confirm the simulations for three cases of BFI and crest length.
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/62376
20170101T00:00:00Z

Development of frequencydependent ocean wave directional distributions
http://hdl.handle.net/10852/62375
Development of frequencydependent ocean wave directional distributions
Simanesew, Abushet; Krogstad, Harald E; Trulsen, Karsten; Nieto Borge, Jose Carlos
The paper discusses the development of a frequency dependent directional spread from an initial condition of frequencyindependence. The study applies basin directional measurements from the Maritime Research Institute Netherlands (MARIN), simulated data from a nonlinear wave equation, and field measurements from the Ekofisk field. The basin experiments and numerical simulations are initialized with a JONSWAP spectrum with frequencyindependent directional distributions. In both cases we observe the development of a strong frequencydependence of the directional spread. The numerical simulations suggest that static nonlinear contributions to the surface elevation partially explain the behavior below the spectral peak in accordance with. There are also dynamic nonlinear contributions on both sides of the spectral peak.
Fri, 01 Jan 2016 00:00:00 GMT
http://hdl.handle.net/10852/62375
20160101T00:00:00Z

Surface wave predictions in weakly nonlinear directional seas
http://hdl.handle.net/10852/62374
Surface wave predictions in weakly nonlinear directional seas
Simanesew, Abushet; Trulsen, Karsten; Krogstad, Harald E; Nieto Borge, José Carlos
We have employed laboratory and numerical experiments in order to investigate propagation of waves in both long and shortcrested wave fields in deep water. For longcrested waves with steepness, ϵ = kcac = 0.1 (a fairly extreme case), reliable prediction can be performed with the modified nonlinear Schrödinger equation up to about 40 characteristic wavelengths. For shortcrested waves the accuracy of prediction is strongly reduced with increasing directional spread.
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/62374
20170101T00:00:00Z

Parameterizing airsea gas transfer velocity with dissipation
http://hdl.handle.net/10852/62373
Parameterizing airsea gas transfer velocity with dissipation
Esters, Leonie; Landwher, Sebastian; Sutherland, Graigory John; Bell, Tom G.; Christensen, Kai Håkon; Saltzman, Eric S.; Miller, Scott D.; Ward, Brian
The airsea gas transfer velocity k is frequently estimated as an empirical function of wind speed. However, it is widely recognized that k depends on processes other than wind speed alone. The smalleddy model, which describes periodic events of small eddies disturbing the sea surface with water from below, suggests a direct relation between k and the dissipation rate of turbulent kinetic energy at the airsea interface. This relation has been proven both in laboratories and in the field in various freshwater and coastal environments, but to date has not been verified in open ocean conditions. Here, concurrent North Atlantic field observations of and eddy covariance measurements of DMS and CO2 airsea gas flux are presented. Using measurements, we compare the smalleddy model at various depths to previously published observations. Extrapolating the measured profiles to the thickness of the viscous sublayer allows us to formulate a function of k that depends solely on the water side friction velocity uw , which can be inferred from direct eddy covariance measurements of the airside friction velocity ua . These field observations are generally consistent with the theoretical smalleddy model. Utilizing a variable Schmidt number exponent in the model, rather than a constant value of 1 2 yields improved agreement between model and observations.
This research was originally published in Journal of Geophysical Research: Oceans. © 2017 Wiley
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/62373
20170101T00:00:00Z

Risk aggregation in Solvency II through recursive lognormals
http://hdl.handle.net/10852/62371
Risk aggregation in Solvency II through recursive lognormals
Bølviken, Erik; Guillen, Montserrat
It is argued that the accuracy of risk aggregation in Solvency II can be improved by updating skewness recursively. A simple scheme based on the lognormal distribution is developed and shown to be superior to the standard formula and to adjustments of the Cornish–Fisher type. The method handles taildependence if a simple Monte Carlo step is included. A hierarchical Clayton copula is constructed and used to confirm the accuracy of the lognormal approximation and to demonstrate the importance of including taildependence. Arguably a lognormal scheme makes the logic in Solvency II consistent, but many other distributions might be used as vehicle, a topic that may deserve further study.
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/62371
20170101T00:00:00Z

The Copula Information Criteria
http://hdl.handle.net/10852/62370
The Copula Information Criteria
Grønneberg, Steffen; Hjort, Nils Lid
We derive two types of Akaike information criterion (AIC)‐like model‐selection formulae for the semiparametric pseudo‐maximum likelihood procedure. We first adapt the arguments leading to the original AIC formula, related to empirical estimation of a certain Kullback–Leibler information distance. This gives a significantly different formula compared with the AIC, which we name the copula information criterion. However, we show that such a model‐selection procedure cannot exist for copula models with densities that grow very fast near the edge of the unit cube. This problem affects most popular copula models. We then derive what we call the cross‐validation copula information criterion, which exists under weak conditions and is a first‐order approximation to exact cross validation. This formula is very similar to the standard AIC formula but has slightly different motivation. A brief illustration with real data is given.
The final version of this research has been published in the Scandinavian Journal of Statistics. © 2014 Wiley
Wed, 01 Jan 2014 00:00:00 GMT
http://hdl.handle.net/10852/62370
20140101T00:00:00Z

Distinct DNA methylation profiles in bone and blood of osteoporotic and healthy postmenopausal women
http://hdl.handle.net/10852/62369
Distinct DNA methylation profiles in bone and blood of osteoporotic and healthy postmenopausal women
Reppe, Sjur; Lien, Tonje Gulbrandsen; Hsu, YiHsiang; Gautvik, Vigdis Teig; Olstad, Ole Kristoffer; Yu, Rona; Bakke, Hege Gilbø; Lyle, Robert; Kringen, Marianne K.; Glad, Ingrid Kristine; Gautvik, Kaare M
DNA methylation affects expression of associated genes and may contribute to the missing genetic effects from genomewide association studies of osteoporosis. To improve insight into the mechanisms of postmenopausal osteoporosis, we combined transcript profiling with DNA methylation analyses in bone. RNA and DNA were isolated from 84 bone biopsies of postmenopausal donors varying markedly in bone mineral density (BMD). In all, 2529 CpGs in the top 100 genes most significantly associated with BMD were analyzed. The methylation levels at 63 CpGs differed significantly between healthy and osteoporotic women at 10% false discovery rate (FDR). Five of these CpGs at 5% FDR could explain 14% of BMD variation. To test whether blood DNA methylation reflect the situation in bone (as shown for other tissues), an independent cohort was selected and BMD association was demonstrated in blood for 13 of the 63 CpGs. Four transcripts representing inhibitors of bone metabolism—MEPE, SOST, WIF1, and DKK1—showed correlation to a high number of methylated CpGs, at 5% FDR. Our results link DNA methylation to the genetic influence modifying the skeleton, and the data suggest a complex interaction between CpG methylation and gene regulation. This is the first study in the hitherto largest number of postmenopausal women to demonstrate a strong association among bone CpG methylation, transcript levels, and BMD/fracture. This new insight may have implications for evaluation of osteoporosis stage and susceptibility.
The final version of this research has been published in Epigenetics. © 2017 Taylor & Francis
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/62369
20170101T00:00:00Z

Model uncertainty first, not afterwards
http://hdl.handle.net/10852/62368
Model uncertainty first, not afterwards
Glad, Ingrid Kristine; Hjort, Nils Lid
Watson and Holmes propose ways of investigating robustness of statistical decisions by examining certain neighbourhoods around a posterior distribution. This may partly amount to ad hoc modelling of extra uncertainty. Instead of creating neighbourhoods around the posterior a posteriori, we argue that it might be more fruitful to model a layer of extra uncertainty first, in the model building process, and then allow the data to determine how big the resulting neighbourhoods ought to be. We develop and briefly illustrate a general strategy along such lines.
Fri, 01 Jan 2016 00:00:00 GMT
http://hdl.handle.net/10852/62368
20160101T00:00:00Z

Weakly Imposed Symmetry and Robust Preconditioners for Biot’s Consolidation Model
http://hdl.handle.net/10852/62357
Weakly Imposed Symmetry and Robust Preconditioners for Biot’s Consolidation Model
Bærland, Trygve; Lee, Jeonghun J.; Mardal, KentAndre; Winther, Ragnar
We discuss the construction of robust preconditioners for finite element approximations of Biot’s consolidation model in poroelasticity. More precisely, we study finite element methods based on generalizations of the Hellinger–Reissner principle of linear elasticity, where the stress tensor is one of the unknowns. The Biot model has a number of applications in science, medicine, and engineering. A challenge in many of these applications is that the model parameters range over several orders of magnitude. Therefore, discretization procedures which are well behaved with respect to such variations are needed. The focus of the present paper will be on the construction of preconditioners, such that the preconditioned discrete systems are wellconditioned with respect to variations of the model parameters as well as refinements of the discretization. As a byproduct, we also obtain preconditioners for linear elasticity that are robust in the incompressible limit.
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/62357
20170101T00:00:00Z

A cellbased framework for numerical modeling of electrical conduction in cardiac tissue
http://hdl.handle.net/10852/62356
A cellbased framework for numerical modeling of electrical conduction in cardiac tissue
Tveito, Aslak; Jæger, Karoline Horgmo; Kuchta, Miroslav; Mardal, KentAndre; Rognes, Marie Elisabeth
In this paper, we study a mathematical model of cardiac tissue based on explicit representation of individual cells. In this EMI model, the extracellular (E) space, the cell membrane (M), and the intracellular (I) space are represented as separate geometrical domains. This representation introduces modeling flexibility needed for detailed representation of the properties of cardiac cells including their membrane. In particular, we will show that the model allows ion channels to be nonuniformly distributed along the membrane of the cell. Such features are difficult to include in classical homogenized models like the monodomain and bidomain models frequently used in computational analyses of cardiac electrophysiology. The EMI model is solved using a finite difference method (FDM) and two variants of the finite element method (FEM). We compare the three schemes numerically, reporting on CPUefforts and convergence rates. Finally, we illustrate the distinctive capabilities of the EMI model compared to classical models by simulating monolayers of cardiac cells with heterogeneous distributions of ionic channels along the cell membrane. Because of the detailed representation of every cell, the computational problems that result from using the EMI model are much larger than for the classical homogenized models, and thus represent a computational challenge. However, our numerical simulations indicate that the FDM scheme is optimal in the sense that the computational complexity increases proportionally to the number of cardiac cells in the model. Moreover, we present simulations, based on systems of equations involving ~117 million unknowns, representing up to ~16,000 cells. We conclude that collections of cardiac cells can be simulated using the EMI model, and that the EMI model enable greater modeling flexibility than the classical monodomain and bidomain models.
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/62356
20170101T00:00:00Z