| Issue |
ESAIM: M2AN
Volume 55, 2021
Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
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|---|---|---|
| Page(s) | S323 - S367 | |
| DOI | https://doi.org/10.1051/m2an/2020043 | |
| Published online | 26 February 2021 | |
Operator splitting around Euler–Maruyama scheme and high order discretization of heat kernels
1
MUFG Bank, Ltd., 2-7-1 Marunouchi, Chiyoda, Tokyo, Japan
2
Hitotsubashi University, 2-1 Naka, Kunitachi, Tokyo, Japan
* Corresponding author: toshihiro.yamada@r.hit-u.ac.jp
Received:
1
July
2019
Accepted:
25
June
2020
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.
Mathematics Subject Classification: 58J35 / 60H07 / 60H30 / 60H35 / 60J60 / 65C05
Key words: Heat kernel / high order discretization / operator splitting / Baker–Campbell–Hausdorff formula / Malliavin calculus
© EDP Sciences, SMAI 2021
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