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

Shigeki Aida, Takanori Kikuchi, Seiichiro Kusuoka

Research output: Contribution to journalArticle

Abstract

We consider the rates of the Lp-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 Lp-convergence are the same as those in the case of the stochastic differential equations of Markovian type without boundaries.

Original languageEnglish
Pages (from-to)65-95
Number of pages31
JournalTohoku Mathematical Journal
Volume70
Issue number1
Publication statusPublished - Mar 1 2018

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Lipschitz condition
Stochastic Equations
Euler
Differential equation
Path
Dependent
Approximation
Boundary conditions
Coefficient

Keywords

  • Euler-maruyama approximation
  • Path-dependent coefficient
  • Rate of convergence
  • Reflecting boundary condition
  • Stochastic differential equation
  • Wong-Zakai approximation

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

The rates of the Lp-convergence of the Euler-Maruyama and Wong-Zakai approximations of path-dependent stochastic differential equations under the Lipschitz condition. / Aida, Shigeki; Kikuchi, Takanori; Kusuoka, Seiichiro.

In: Tohoku Mathematical Journal, Vol. 70, No. 1, 01.03.2018, p. 65-95.

Research output: Contribution to journalArticle

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