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(Research report / Forskningsrapport, 2003)
We propose a Kruzkov-type entropy condition for nonlinear degenerate parabolic equations with discointinuous coefficients. We establish L1 stability, and thus uniqueness, for weak solutions satisfying the entropy condition, ...
(Research report / Forskningsrapport, 2003)
In this work we characterize the smooth surfaces which can be embedded in the Grassmannian G(1,5) with one apparent double point, i.e. such that the general projection to G(1,3) produces just one double point. The result ...
(Research report / Forskningsrapport, 2003)
The Dirichlet process has been extensively studied over the last thirty years, along with various generalisations, and remains a fundamental tool for nonparametric Bayesian statistics. The probabilistic structure of its ...
(Research report / Forskningsrapport, 2003)
We consider a scalar conservation law modeling the settling of particles in an ideal clarifier-thickener unit. The conservation law has a nonconvex flux which is spatially dependent on two discontinuous parameters. We ...
(Research report / Forskningsrapport, 2003)
We give a survey of the stochastic calculus of fractional Brownian motion, and we discuss its applications to financial markets where the prices are described as solutions of stochastic differential equations driven by ...
(Research report / Forskningsrapport, 2003)
We determine a new explicit representation of the strong solution of Itô-diffusions and elicit its correspondence to the general stochastic transport equation. We apply this formula to deduce an explicit Donsker delta ...
(Research report / Forskningsrapport, 2003)
We give an explicit representation of strong solutions of Itô-SDE's in Hilbert spaces in terms of a non linear operation on a stochastic distribution space. This formula can be potentially used to obtain solutions of SDE's ...
(Research report / Forskningsrapport, 2003)
We prove well posedness (existence and uniqueness) of renormalized entropy solutions to the Cauchy problem for quasilinear anisotropic degenerate parabolic equations with L1 data. This paperÊ complements the work by Chen ...
(Research report / Forskningsrapport, 2003)
This Statistical Research Report contains the complete written discussion generated by the two papers “Frequentist Model Average Estimators”, by Hjort and Claeskens, and “The Focussed Information Criterion”, by Claeskens ...
(Research report / Forskningsrapport, 2003)
(Research report / Forskningsrapport, 2003)
In this paper we explicitly solve a non-linear filtering problem with mixed observations, modelled by a Brownian motion and a generalized Cox process, whose jump intensity is given in terms of a Lévy measure. Motivated by ...
(Research report / Forskningsrapport, 2003)
(Research report / Forskningsrapport, 2002)
(Research report / Forskningsrapport, 2002)
(Research report / Forskningsrapport, 2002)
It is well known that a wide range of impulse control problems are continuous, but not differentiable, with respect to intervention cost as it approaches zero. We show a similar non-C1 result, assuming that the problem and ...
(Research report / Forskningsrapport, 2002)
In this paper we define a class of MCMC algorithms, the generalized self regenerative chains (GSR), generalizing the SR chain of Sahu and Zhigljavski (2001), which contains rejection sampling as a special case. We show ...
(Research report / Forskningsrapport, 2002)
(Research report / Forskningsrapport, 2002)
This paper shows a version of Arrow's generalization of Mangasarian's sufficient conditions valid for controlled stochastic differential equations driven by semimartingales. The infinite case is covered. An example is given.
(Research report / Forskningsrapport, 2002)
We develop an anticipative calculus for Lévy processes with finite second moment. The calculus is based on the chaos expansion of square-integrable random variables in terms of iterated integrals of the compensated Poisson ...
(Research report / Forskningsrapport, 2002)
The basic multistate reliability theory was developed in the eighties and the beginning of the nineties, replacing traditional reliability theory where the system and the components are always described as functioning or ...
(Research report / Forskningsrapport, 2002)
Multi-state models are used to describe situations where individuals may move among a finite number of states defined by specific conditions of health, including death. The transition intensities of the models are described ...
(Research report / Forskningsrapport, 2002)
The stability of barotropic and baroclinic shelf slope currents currents is investigated. Assuming periodic small amplitude perturbation in along shelf direction the stability problem is reduced to an eigenvalue problem ...
(Research report / Forskningsrapport, 2002)
We discuss the extension to the multi-dimensional case of the Wick-Itô integral with respect to fractional Brownian motion, introduced by [DHP] in the 1-dimensional case. We prove a multi-dimensional Itô type isometry for ...
(Research report / Forskningsrapport, 2002)
(Research report / Forskningsrapport, 2002)
(Research report / Forskningsrapport, 2002)
This is part two of a work on adaptive integration methods aimed at multidimensional option pricing problems in finance. It presents simulation results of an adaptive method developed in a companion article for the evaluation ...
(Research report / Forskningsrapport, 2002)
For stochastic functions over the product of a general space and a time interval, the standard type non-anticipating integration scheme is applied with respect to the stochastic measures with independent values. In this ...
(Research report / Forskningsrapport, 2002)
Second order effects of axial forces on displacements in compression members are small and can be neglected in a great many structures, which may then be designed for forces obtained by conventional first order theory. ...
(Research report / Forskningsrapport, 2002)
(Research report / Forskningsrapport, 2002)
Effects of axial forces on the displacements in compression members, generally termed second order effects, are small and can be neglected in a great many structures. In recognition of this, most design codes and standards ...
(Research report / Forskningsrapport, 2002)
The paper presents an adaptive method for the evaluation of multidimensional integrals over the unit cube. The measure used to partition the domain is suited for integrands which are monotonic in each dimension individually, ...
(Research report / Forskningsrapport, 2002)
We develop a white noise calculus for pure jump Lévy processes on Poisson space. This theory covers the treatment of Lévy processes of unbounded variation. The starting point of the theory is a novel construction of a ...
(Research report / Forskningsrapport, 2002)
Let G be a finite p-group. The problem whether (the isomorphism class of) G is determined by its group algebra over the field of p elements (the modular group algebra) is usually referred to as the modular isomorphism ...
(Research report / Forskningsrapport, 2002)
In this paper we investigate the recently introduced Malliavin approach compared to more classical approaches to find sensitivities of options in commodity and energy markets. The Malliavin approach has been developed in ...
(Research report / Forskningsrapport, 2002)
In this paper we develop a white noise framework for the study of stochastic partial differential equations driven by a d-parameter (pure jump) Lévy white noise. As an example we use this theory to solve the stochastic ...
(Research report / Forskningsrapport, 2002)
We show that the isomorphism class of a finite p-group G is determined by the group algebra of G over the field of p elements, hence solving the modular isomorphism problem.
(Research report / Forskningsrapport, 2002)
(Research report / Forskningsrapport, 2002)
We develop a white noise theory for Poisson random measures associated with a Lévy process. The starting point of this theory is a chaos expansion with kernels of polynomial type. We use this to construct the white noise ...
(Research report / Forskningsrapport, 2001)
It is suggested that inference under the proportional hazard model can be carried out by programs for exact inference under the logistic regression model. Furthermore a different type of exact inference is developed under ...
(Research report / Forskningsrapport, 2001)
In this article we classify all the smooth 3-folds of P5 with an apparent 4-tuple point provided that the family of its 4-secant lines is an irreducible (first order) congruence. This is sufficient to conclude the ...
(Research report / Forskningsrapport, 2001)
In this note we consider the asymptotic power functions of some bootstrap unit root tests under local alternatives and show that they are in fact the same as for ordinary unit root tests. This is regardless of whether the ...
(Research report / Forskningsrapport, 2001)
We continue our study of the concepts of amenability and co-amenability for algebraic quantum groups in the sense of A. Van Daele and our investigation of their relationship with nuclearity and injectivity. One major tool ...
(Research report / Forskningsrapport, 2001)
We consider optimal control problems where the state X(t) at time t of the system is given by a stochastic differential delay equation. The growth at time t not only depends on the present value X(t), but also on X(t-d) ...
(Research report / Forskningsrapport, 2001)
We define concepts of amenability and co-amenability for algebraic quantum groups in the sense of A. Van Daele [21]. We show that co-amenability of an algebraic quantum group always implies amenability of its dual. Various ...
(Research report / Forskningsrapport, 2001)
(Research report / Forskningsrapport, 2001)
This paper focus on experiments on run-up of strongly nonlinear waves on a moderately steep beach of 10.5deg inclination. Velocity fields are obtained by the PIV (Particle Image Velocimetry) technique. Acceleration ...
(Research report / Forskningsrapport, 2001)
Background: According to published data, the ability to prevent various hypertension related events differs between the various anti-hypertensive drug groups. Although absolute drug effects with similar drugs also differ ...
(Research report / Forskningsrapport, 2001)
This survey is intended for estimating several types of copyright volume at different educational institutions in Norway. Using a calibration factor being equal to the ratio of the true number of machine pages taken from ...
(Research report / Forskningsrapport, 2001)
In the present paper we investigate three classes of reliability systems: regular clutters, total amenable clutters and clutters where a certain factoring strategy for computing reliability is in a sense optimal. In the ...
(Research report / Forskningsrapport, 2001)
An industrial Navier-Stokes solver (FLUENT) is used to examine steep waves as they run up a steep beach (10.54$^0$). The volume of fluid method (VOF) is used to model the free surface. Comparison with experimental results ...
(Research report / Forskningsrapport, 2001)
We formulate generation of tsunamis by earthquakes as a linear potential flow problem with rapid in and out-flux at the sea bottom. Starting from solutions for a few simplified bottom deformations we proceed to establish ...
(Research report / Forskningsrapport, 2001)
In the present report we describe the geometrically nonlinear method for orthotropic (composite) materials that is implemented using the commercial C++ library Diffpack. The implementation is based on a module dealing with ...
(Research report / Forskningsrapport, 2001)
(Research report / Forskningsrapport, 2001)
We give a short introduction to some of the theory and methods involved in We prove a verification theorem for a class of singular control problems which model optimal harvesting with density-dependent prices or optimal ...
(Research report / Forskningsrapport, 2001)
We prove an existence and uniqueness result for a general class of backward stochastic partial differential equations. This is a type of equations which appear as adjoint equations in the maximum principle approach to ...
(Research report / Forskningsrapport, 2001)
(Research report / Forskningsrapport, 2001)
The problem of irreversibly harvesting from a general one dimensional (Wiener-Poisson) jump diffusion population model is studied. For a wide class of models, including stochastic generalizations of the logistic model ...
(Research report / Forskningsrapport, 2001)
When portfolio choice in discontinuous asset price models is considered, the possibility of a jump to 0 is often overlooked. We solve the Merton problem for a (modified) HARA agent in a geometric Lévy market where the ...
(Research report / Forskningsrapport, 2001)
We give a verification theorem by employing Arrow's generalization of the Mangasarian sufficient condition to a general jump diffusion setting, and show the adjoint processes' connections to dynamic programming. The result ...
(Research report / Forskningsrapport, 2001)
We introduce and study several amenability properties for unitary corepresentations and *-representations of algebraic quantum groups, which may be used to characterize amenability or co-amenability of such groups. As a ...
(Research report / Forskningsrapport, 2001)
A Meyer-Tanaka formula involving weighted local time is derived for fractional Brownian motion and geometric fractional Brownian motion. The formula is applied to the study of the stop-loss-start-gain (SLSG) portfolio in ...
(Research report / Forskningsrapport, 2001)
For a wide class of models concerning the optimal harvesting of a natural resource, an expected profit maximizer will not deplete the resource completely if its relative growth rate is strictly greater than the interest ...
(Research report / Forskningsrapport, 2001)
We prove a sufficient maximum principle for the optimal control of systems described by a quasilinear stochastic heat equation. The result is applied to give a maximum principle solution method for stochastic control ...
(Research report / Forskningsrapport, 2001)
The problem of simultaneous decomposition of binary forms as sums of powers of linear forms is studied. For generic forms the minimal number of linear forms needed is found and the space parametrizing all the possible ...
(Research report / Forskningsrapport, 2001)
In a preceding paper, [7], physical optics was developed for a selection of discrete long wave solutions by application a perturbation expansion. Herein, we approach discrete optics from analysis of discrete energy, in the ...
(Research report / Forskningsrapport, 2001)
In a market driven by a Lévy martingale, we consider a claim x. We study the problem of minimal variance hedging and we give an explicit formula for the minimal variance portfolio in terms of Malliavin derivatives. We ...
(Research report / Forskningsrapport, 2001)
The stochastic integral representation for an arbitrary random variable in a standard $L_2$-space is considered in a case of a general $L_2$-continuous martingale as integrator. In relation to this, a certain stochastic ...
(Research report / Forskningsrapport, 2001)
(Research report / Forskningsrapport, 2001)
We give a short introduction to some of the theory and methods involved in stochastic control with partial observation. As an illustration we use the stochastic maximum principle and the Kalman-Bucy filter to solve explicitly ...
(Research report / Forskningsrapport, 2001)
We investigate a class of optimal consumption problems where the wealth X(t) at time t is given by a stochastic differential delay equation with a parameter. Not only the present value X(t), but also X(t-\delta) and some ...
(Research report / Forskningsrapport, 2001)
While it is common knowledge that portfolio separation in a continuous-time lognormal market is due to the basic properties of the normal distribution, the usual exposition found in text books relies on dynamic programming ...
(Research report / Forskningsrapport, 2001)
(Research report / Forskningsrapport, 2001)
(Research report / Forskningsrapport, 2001)
(Research report / Forskningsrapport, 2000)
(Research report / Forskningsrapport, 2000)
(Research report / Forskningsrapport, 2000)
(Research report / Forskningsrapport, 2000)
(Research report / Forskningsrapport, 2000)
(Research report / Forskningsrapport, 2000)
(Research report / Forskningsrapport, 2000)
(Research report / Forskningsrapport, 2000)
(Research report / Forskningsrapport, 2000)
(Research report / Forskningsrapport, 2000)
(Research report / Forskningsrapport, 2000)
(Research report / Forskningsrapport, 2000)
(Research report / Forskningsrapport, 2000)
(Research report / Forskningsrapport, 2000)
(Research report / Forskningsrapport, 2000)
(Research report / Forskningsrapport, 2000)
(Research report / Forskningsrapport, 2000)
(Research report / Forskningsrapport, 2000)
(Research report / Forskningsrapport, 2000)
Two new different stochastic models for earthquake occurrence are discussed. Both models are focusing on the spatio-temporal interactions between earthquakes. The parameters of the models are estimated from a Bayesian ...
(Research report / Forskningsrapport, 2000)
(Research report / Forskningsrapport, 2000)
(Research report / Forskningsrapport, 2000)
(Research report / Forskningsrapport, 2000)
(Research report / Forskningsrapport, 2000)
Multiparameter fractional Brownian motion and quasi-linear stochastic partial differential equations
(Research report / Forskningsrapport, 2000)
(Research report / Forskningsrapport, 2000)