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Stochastic Distribution Processes with applications to Stochastic Differential Equations Driven by Lévy White Noise

Røse, Elin Engen
Master thesis
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Year
2010
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http://urn.nb.no/URN:NBN:no-26898

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  • Matematikk [203]
Abstract
We regard a stochastic process as a weakly measurable function, taking values one of the Kondratiev Stochastic distribution spaces, (S)_{-\rho}. Since these spaces are duals of nuclear spaces, functions taking values in the dual of a nuclear space are treated in detail.

The space (S)_{-1} is a topological algebra with respect to the Wick product, ⋄, and the following relation hold,

∫Y(s)δη(s)=∫Y(s)⋄\dot{η}(s)ds.

As a consequence, we can regard SDEs as (S)_{-1}-valued ODEs. Similarily, we will regard an SPDE as an (S)_{-1}-valued PDE.
 
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