Operator splitting around Euler–Maruyama scheme and high order discretization of heat kernels
- Resource Type
- Authors
- Yuga Iguchi; Toshihiro Yamada
- Source
- ESAIM: Mathematical Modelling and Numerical Analysis. 55:S323-S367
- Subject
- Numerical Analysis
Discretization
Applied Mathematics
010103 numerical & computational mathematics
Malliavin calculus
01 natural sciences
010104 statistics & probability
Computational Mathematics
symbols.namesake
Baker–Campbell–Hausdorff formula
Modeling and Simulation
Fundamental solution
Euler's formula
symbols
Order operator
Applied mathematics
Heat equation
0101 mathematics
Analysis
Heat kernel
Mathematics
- Language
- ISSN
- 1290-3841
0764-583X
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.