Tohoku Mathematical Journal

The rates of the $L^p$-convergence of the Euler-Maruyama and Wong-Zakai approximations of path-dependent stochastic differential equations under the Lipschitz condition

Shigeki Aida, Takanori Kikuchi, and Seiichiro Kusuoka

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Abstract

We consider the rates of the $L^p$-convergence of the Euler-Maruyama and Wong-Zakai approximations of path-dependent stochastic differential equations under the Lipschitz condition on the coefficients. By a transformation, the stochastic differential equations of Markovian type with reflecting boundary condition on sufficiently good domains are to be associated with the equations concerned in the present paper. The obtained rates of the $L^p$-convergence are the same as those in the case of the stochastic differential equations of Markovian type without boundaries.

Article information

Source
Tohoku Math. J. (2), Volume 70, Number 1 (2018), 65-95.

Dates
First available in Project Euclid: 9 March 2018

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1520564419

Digital Object Identifier
doi:10.2748/tmj/1520564419

Mathematical Reviews number (MathSciNet)
MR3772806

Zentralblatt MATH identifier
06873674

Subjects
Primary: 60H10: Stochastic ordinary differential equations [See also 34F05]
Secondary: 65C30: Stochastic differential and integral equations

Keywords
stochastic differential equation reflecting boundary condition path-dependent coefficient Euler-Maruyama approximation Wong-Zakai approximation rate of convergence

Citation

Aida, Shigeki; Kikuchi, Takanori; Kusuoka, Seiichiro. The rates of the $L^p$-convergence of the Euler-Maruyama and Wong-Zakai approximations of path-dependent stochastic differential equations under the Lipschitz condition. Tohoku Math. J. (2) 70 (2018), no. 1, 65--95. doi:10.2748/tmj/1520564419. https://projecteuclid.org/euclid.tmj/1520564419


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