Weak approximation of SDEs for tempered distributions and applications. (English) Zbl 1498.60189
Summary: 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.
MSC:
| 60H07 | Stochastic calculus of variations and the Malliavin calculus |
| 60H30 | Applications of stochastic analysis (to PDEs, etc.) |
| 60H35 | Computational methods for stochastic equations (aspects of stochastic analysis) |
| 60J60 | Diffusion processes |
| 65C05 | Monte Carlo methods |
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