Finite difference schemes for stochastic partial differential equations in Sobolev spaces

Abstract

We discuss $L_p$-estimates for finite difference schemes approximating parabolic, possibly degenerate, SPDEs, with initial conditions from $W_p^m$ and free terms taking values in $W_p^m.$ Consequences of these estimates include an asymptotic expansion of the error, allowing the acceleration of the approximation by Richardson's method.

22 pages. The final publication is available at Springer via http://dx.doi.org/10.1007/s00245-014-9272-2

References in corpus (2)

• Rate of Convergence of Space Time Approximations for stochastic evolution equations
• Accelerated spatial approximations for time discretized stochastic partial differential equations

Cited by in corpus (3)

• On the solvability of degenerate stochastic partial differential equations in Sobolev spaces
• A Feynman-Kac formula for stochastic Dirichlet problems
• Strong convergence of parabolic rate $1$ of discretisations of stochastic Allen-Cahn-type equations