A New Discretization Scheme for One Dimensional Stochastic Differential Equations Using Time Change Method

Masaaki Fukasawa; Mitsumasa Ikeda

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arXiv · 2006.02626

A New Discretization Scheme for One Dimensional Stochastic Differential Equations Using Time Change Method

Masaaki Fukasawa·Mitsumasa Ikeda

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Abstract

We propose a new numerical method for one dimensional stochastic differential equations (SDEs). The main idea of this method is based on a representation of a weak solution of a SDE with a time changed Brownian motion, dated back to Doeblin (1940). In cases where the diffusion coefficient is bounded and $\beta$-H\"{o}lder continuous with $0 < \beta \leq 1$, we provide the rate of strong convergence. An advantage of our approach is that we approximate the weak solution, which enables us to treat a SDE with no strong solution. Our scheme is the first to achieve the strong convergence for the case $0 < \beta < 1/2$.

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Masaaki Fukasawa, Mitsumasa Ikeda. 2020-06-04. A New Discretization Scheme for One Dimensional Stochastic Differential Equations Using Time Change Method. https://arxiv.org/abs/2006.02626

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