Weak approximation of SDEs for tempered distributions and applications

Iguchi, Y. and Yamada, Toshihiro (2022) Weak approximation of SDEs for tempered distributions and applications. Advances in Computational Mathematics, 48: 52. ISSN 1019-7168

Abstract

The paper shows a new weak approximation for generalized expectation of composition of a Schwartz tempered distribution and a solution to stochastic differential equation. Any order discretization is provided by using stochastic weights which do not depend on the Schwartz distribution. The error bound is obtained through stochastic analysis, which is consistent with the results of numerical experiments. It can also be confirmed that the proposed approximation gives high numerical accuracy.