Operator splitting around Euler–Maruyama scheme and high order discretization of heat kernels.
- Resource Type
- Article
- Authors
- Iguchi, Yuga; Yamada, Toshihiro
- Source
- ESAIM: Mathematical Modelling & Numerical Analysis (ESAIM: M2AN). 2021 Supplement, Vol. 55, pS323-S367. 45p.
- Subject
- *MALLIAVIN calculus
*DIFFUSION processes
*HEAT equation
*NONCOMMUTATIVE algebras
*DISCRETIZATION methods
- Language
- ISSN
- 2822-7840
This paper proposes a general higher order operator splitting scheme for diffusion semigroups using the Baker–Campbell–Hausdorff type commutator expansion of non-commutative algebra and the Malliavin calculus. An accurate discretization method for the fundamental solution of heat equations or the heat kernel is introduced with a new computational algorithm which will be useful for the inference for diffusion processes. The approximation is regarded as the splitting around the Euler–Maruyama scheme for the density. Numerical examples for diffusion processes are shown to validate the proposed scheme. [ABSTRACT FROM AUTHOR]