Weak order for the discretization of the stochastic heat equation driven by impulsive noise

Details Weak order for the discretization of the stochastic heat equation driven by impulsive noise Weak order for the discretization of the stochastic heat equation driven by impulsive noise

2009-11-24

arxiv.org/abs/0911.4681v2

Mathematics

Probability

29 pages; Section 1 extended, new results in Appendix B

Scientific paper

Considering a linear parabolic stochastic partial differential equation driven by impulsive space time noise, dX_t+AX_t dt= Q^{1/2}dZ_t, X_0=x_0\in H, t\in [0,T], we approximate the distribution of X_T. (Z_t)_{t\in[0,T]} is an impulsive cylindrical process and Q describes the spatial covariance structure of the noise; Tr(A^{-\alpha})<\infty for some \alpha>0 and A^\beta Q is bounded for some \beta\in(\alpha-1,\alpha]. A discretization (X_h^n)_{n\in\{0,1,...,N\}} is defined via the finite element method in space (parameter h>0) and a \theta-method in time (parameter \Delta t=T/N). For \phi\in C^2_b(H;R) we show an integral representation for the error |E\phi(X^N_h)-E\phi(X_T)| and prove that |E\phi(X^N_h)-E\phi(X_T)|=O(h^{2\gamma}+(\Delta t)^{\gamma}) where \gamma<1-\alpha+\beta.

Affiliated with

Also associated with

No associations

Rating

Weak order for the discretization of the stochastic heat equation driven by impulsive noise does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Weak order for the discretization of the stochastic heat equation driven by impulsive noise, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Weak order for the discretization of the stochastic heat equation driven by impulsive noise will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-280280