Download This PaperOperator Splitting Around Euler-Maruyama Scheme and High Order Discretization of Heat Kernels
40 Pages Posted: 16 Jan 2020 Last revised: 31 Jul 2020
Date Written: July 1, 2019
Abstract
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.
Keywords: Heat kernel, High order discretization, Operator splitting, Baker-Campbell- Hausdorff formula, Malliavin calculus
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