Erika Hausenblas

Numerical analysis of semilinear stochastic evolution equations in Banach spaces

The solution of stochastic evolution equations generally relies on numerical computation. Here, usually the main idea is to discretize the SPDE spatially obtaining a system of SDEs that can be solved by e.g., the Euler scheme. In this paper, we investigate the discretization error of semilinear stochastic evolution equations in Lp-spaces, resp. Banach spaces. The space discretization may be done by Galerkin approximation, for the time discretization we consider the implicit Euler, the explicit Euler scheme and the Crank-Nicholson scheme. In the last section, we give some examples i.e., we consider an SPDEs driven by nuclear Wiener noise approximated by wavelets and delay equation approximated by finite differences.

Error Analysis for Approximation of Stochastic Differential Equations Driven by Poisson Random Measures

Let Xt be the solution of a stochastic differential equation (SDE) with starting point x0 driven by a Poisson random measure. Additive functionals are of interest in various applications. Nevertheless they are often unknown and can only be found by simulation on computers. We investigate the quality of the Euler approximation. Our main emphasis is on SDEs driven by an

Stochastic Reaction-diffusion Equations Driven by Jump Processes

\alpha

Approximate Euler Method for Parabolic Stochastic Partial Differential Equations Driven by Space-Time Lévy Noise

-stable process,

Uniqueness in Law of the Itô Integral with Respect to Lévy Noise

0<\alpha < 2

Numerical approximation of stochastic evolution equations : convergence in scale of Hilbert spaces

, where we study the approximation of the Monte Carlo error

Time-Splitting Methods to Solve the Stochastic Incompressible Stokes Equation

{\Bbb E} [f(X_T)]

Pathwise space approximations of semi-linear parabolic SPDEs with multiplicative noise

, f belonging to

Ergodicity of Stochastic Shell Models Driven by Pure Jump Noise

{L}^\infty

Copulas in Hilbert spaces

. Moreover, we treat the case where the time equals