The weak rate of convergence for the Euler-Maruyama approximation of one-dimensional stochastic differential equations involving the local times of the unknown process

Mohsine Benabdallah; Kamal Hiderah

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arXiv · 1701.00551

The weak rate of convergence for the Euler-Maruyama approximation of one-dimensional stochastic differential equations involving the local times of the unknown process

Mohsine Benabdallah·Kamal Hiderah

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Abstract

In this paper, we consider the weak convergence of the Euler-Maruyama approximation for one dimensional stochastic differential equations involving the local times of the unknown process. We use a transformation in order to remove the local time from the stochastic differential equations and we provide the approximation of Euler-maruyama for the stochastic differential equations without local time. After that, we conclude the approximation of Euler-maruyama for one dimensional stochastic differential equations involving the local times of the unknown process , and we provide the rate of weak convergence for any function G in a certain class.

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BibTeX RIS

Mohsine Benabdallah, Kamal Hiderah. 2017-01-02. The weak rate of convergence for the Euler-Maruyama approximation of one-dimensional stochastic differential equations involving the local times of the unknown process. https://arxiv.org/abs/1701.00551

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