### 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.

Original language | English |
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Pages (from-to) | 65-95 |

Number of pages | 31 |

Journal | Tohoku Mathematical Journal |

Volume | 70 |

Issue number | 1 |

Publication status | Published - Mar 1 2018 |

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### 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

^{p}-convergence of the Euler-Maruyama and Wong-Zakai approximations of path-dependent stochastic differential equations under the Lipschitz condition.

*Tohoku Mathematical Journal*,

*70*(1), 65-95.

**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.** / Aida, Shigeki; Kikuchi, Takanori; Kusuoka, Seiichiro.

Research output: Contribution to journal › Article

^{p}-convergence of the Euler-Maruyama and Wong-Zakai approximations of path-dependent stochastic differential equations under the Lipschitz condition',

*Tohoku Mathematical Journal*, vol. 70, no. 1, pp. 65-95.

^{p}-convergence of the Euler-Maruyama and Wong-Zakai approximations of path-dependent stochastic differential equations under the Lipschitz condition. Tohoku Mathematical Journal. 2018 Mar 1;70(1):65-95.

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TY - JOUR

T1 - The rates of the Lp-convergence of the Euler-Maruyama and Wong-Zakai approximations of path-dependent stochastic differential equations under the Lipschitz condition

AU - Aida, Shigeki

AU - Kikuchi, Takanori

AU - Kusuoka, Seiichiro

PY - 2018/3/1

Y1 - 2018/3/1

N2 - 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.

AB - 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.

KW - Euler-maruyama approximation

KW - Path-dependent coefficient

KW - Rate of convergence

KW - Reflecting boundary condition

KW - Stochastic differential equation

KW - Wong-Zakai approximation

UR - http://www.scopus.com/inward/record.url?scp=85045676658&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85045676658&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85045676658

VL - 70

SP - 65

EP - 95

JO - Tohoku Mathematical Journal

JF - Tohoku Mathematical Journal

SN - 0040-8735

IS - 1

ER -