Let X be the mild solution of a stochastic heat equation taking values in a Hilbert space H=L^2((0,1)^d) driven by a (cylindrical) Brownian motion W with values in H. We study the strong approximation of X at a fixed time point t=T for equations with additive noise. The algorithms we consider, are based on evaluations of a finite number of one-dimensional components of W at a finite number of time nodes. For the first time, non-equidistant time discretizations are considered. We analyze the smallest possible error obtained by arbitrary algorithms that use at most a total of N evaluations. The main results of this thesis are the derivation of the weak asymptotic of these minimal errors, depending on the spatial dimension d and the smoothness...
We present an abstract framework for analyzing the weak error of fully discrete approximation scheme...
The stochastic heat equation on the sphere driven by additive isotropic Wiener noise is approximated...
AbstractWe study linear stochastic evolution partial differential equations driven by additive noise...
Let X be the mild solution of a stochastic heat equation taking values in a Hilbert space H=L^2((0,1...
We study algorithms for approximation of the mild solution of stochastic heat equations on the spat...
Abstract. We study algorithms for approximation of the mild solution of stochastic heat equations on...
We find the weak rate of convergence of approximate solutions of the nonlinear stochastic heat equat...
This article establishes optimal upper and lower error estimates for strong full-discrete numerical ...
We consider a stochastic evolution equation on the spatial domain D=(0,1)^d, driven by an additive n...
We apply the well-known Banach–Nečas–Babuška inf–sup theory in a stochastic setting to introduce a w...
We show that a large class of stochastic heat equations can be approximated by systems of interactin...
AbstractWe study pathwise approximation of scalar stochastic differential equations. The mean square...
International audienceIn this paper we study the approximation of the distribution of $X_t$ Hilbert-...
Semidiscrete finite element approximation of the linear stochastic wave equation (LSWE) with additiv...
We present an abstract framework for analyzing the weak error of fully discrete approximation scheme...
The stochastic heat equation on the sphere driven by additive isotropic Wiener noise is approximated...
AbstractWe study linear stochastic evolution partial differential equations driven by additive noise...
Let X be the mild solution of a stochastic heat equation taking values in a Hilbert space H=L^2((0,1...
We study algorithms for approximation of the mild solution of stochastic heat equations on the spat...
Abstract. We study algorithms for approximation of the mild solution of stochastic heat equations on...
We find the weak rate of convergence of approximate solutions of the nonlinear stochastic heat equat...
This article establishes optimal upper and lower error estimates for strong full-discrete numerical ...
We consider a stochastic evolution equation on the spatial domain D=(0,1)^d, driven by an additive n...
We apply the well-known Banach–Nečas–Babuška inf–sup theory in a stochastic setting to introduce a w...
We show that a large class of stochastic heat equations can be approximated by systems of interactin...
AbstractWe study pathwise approximation of scalar stochastic differential equations. The mean square...
International audienceIn this paper we study the approximation of the distribution of $X_t$ Hilbert-...
Semidiscrete finite element approximation of the linear stochastic wave equation (LSWE) with additiv...
We present an abstract framework for analyzing the weak error of fully discrete approximation scheme...
The stochastic heat equation on the sphere driven by additive isotropic Wiener noise is approximated...
AbstractWe study linear stochastic evolution partial differential equations driven by additive noise...