abstract:
First, I would like to introduce Levy processes, respective Poisson random measures,
and stochastic integration with respect to Levy processes, in particular, stochastic integration in Banach
spaces. \\
The second part of the talk will be about existence and uniqueness of SPDEs. Here, I will point out the techniques which are used and
present some results. \\
In the third and last part of the talk I will speak abut the numerical approximation of SPDEs,
in particular, of SPDEs driven by Levy processes. \\
The talk will be based on the following works [1--3]:
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[1] & {\sc E. Hausenblas}:
Existence, uniqueness and regularity of parabolic SPDEs driven by Poisson random measure.
{\it Electron. J. Probab.}, {\bf 10}, (2005), 1496--1546. \\
[2] & {\sc E. Hausenblas}: Finite element approximation of stochastic partial differential equations driven by Poisson random measures of jump type.
{\it SIAM J. Numer. Anal.}
{\bf 46} (2007/08), 437--471. \\
[3] & {\sc E. Hausenblas, T.\ Dunst}: Numerical experiments concerning
Finite element approximation of stochastic partial differential equations driven by Poisson random measures . {\it In preparation}, (2009). \bigskip
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