Euler schemes and large deviations for stochastic Volterra equations with singular kernels

Xicheng Zhang

doi:10.1016/j.jde.2008.02.019

Euler schemes and large deviations for stochastic Volterra equations with singular kernels

Xicheng Zhang^*

^*Corresponding author for this work

Huazhong University of Science and Technology

Research output: Contribution to journal › Article › peer-review

105 Citations (Scopus)

Abstract

In this paper, an Euler type approximation is constructed for stochastic Volterra equation with singular kernels, which provides an algorithm for numerical calculation. Then, the large deviation estimates of small perturbation to equations of this type are obtained. We finally apply them to SDEs with the kernel of fractional Brownian motion with Hurst parameter H ∈ (0, 1).

Original language	English
Pages (from-to)	2226-2250
Number of pages	25
Journal	Journal of Differential Equations
Volume	244
Issue number	9
DOIs	https://doi.org/10.1016/j.jde.2008.02.019
Publication status	Published - 1 May 2008
Externally published	Yes

Keywords

Euler scheme
Fractional Brownian motion
Large deviation
Stochastic Volterra equation

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10.1016/j.jde.2008.02.019

Cite this

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title = "Euler schemes and large deviations for stochastic Volterra equations with singular kernels",

abstract = "In this paper, an Euler type approximation is constructed for stochastic Volterra equation with singular kernels, which provides an algorithm for numerical calculation. Then, the large deviation estimates of small perturbation to equations of this type are obtained. We finally apply them to SDEs with the kernel of fractional Brownian motion with Hurst parameter H ∈ (0, 1).",

keywords = "Euler scheme, Fractional Brownian motion, Large deviation, Stochastic Volterra equation",

author = "Xicheng Zhang",

year = "2008",

month = may,

day = "1",

doi = "10.1016/j.jde.2008.02.019",

language = "English",

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T1 - Euler schemes and large deviations for stochastic Volterra equations with singular kernels

AU - Zhang, Xicheng

PY - 2008/5/1

Y1 - 2008/5/1

N2 - In this paper, an Euler type approximation is constructed for stochastic Volterra equation with singular kernels, which provides an algorithm for numerical calculation. Then, the large deviation estimates of small perturbation to equations of this type are obtained. We finally apply them to SDEs with the kernel of fractional Brownian motion with Hurst parameter H ∈ (0, 1).

AB - In this paper, an Euler type approximation is constructed for stochastic Volterra equation with singular kernels, which provides an algorithm for numerical calculation. Then, the large deviation estimates of small perturbation to equations of this type are obtained. We finally apply them to SDEs with the kernel of fractional Brownian motion with Hurst parameter H ∈ (0, 1).

KW - Euler scheme

KW - Fractional Brownian motion

KW - Large deviation

KW - Stochastic Volterra equation

UR - https://www.scopus.com/pages/publications/41149145034

U2 - 10.1016/j.jde.2008.02.019

DO - 10.1016/j.jde.2008.02.019

M3 - Article

AN - SCOPUS:41149145034

SN - 0022-0396

VL - 244

SP - 2226

EP - 2250

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 9

ER -

Euler schemes and large deviations for stochastic Volterra equations with singular kernels

Abstract

Keywords

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