A convergence result for stochastic partial differential equations

Abstract

For regular approximations w_nof the Brownian motion wthe solutions of the PDE converge to the unique solution of the stochastic partial differential equation . The assumptions on the operators A and B are not restrictive including for instance random,A, and admit physically meaningful applications.

Keywords:

• Stochastic partial differential equation
• convergence
• semigroups
• white noise
• pathwise solutions

^∗The Research of this Author Was Partially Supported by SERC Grant. His Present Address: Department of Pure Mathematics, University of Hull, Hull, England

^∗The Research of this Author Was Partially Supported by SERC Grant. His Present Address: Department of Pure Mathematics, University of Hull, Hull, England

Notes

^∗The Research of this Author Was Partially Supported by SERC Grant. His Present Address: Department of Pure Mathematics, University of Hull, Hull, England