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^*

^*此作品的通讯作者

Huazhong University of Science and Technology

科研成果: 期刊稿件 › 文章 › 同行评审

85 引用（Scopus）

摘要

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).

源语言	英语
页（从-至）	2226-2250
页数	25
期刊	Journal of Differential Equations
卷	244
期	9
DOI	https://doi.org/10.1016/j.jde.2008.02.019
出版状态	已出版 - 1 5月 2008
已对外发布	是

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10.1016/j.jde.2008.02.019

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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",

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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

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JO - Journal of Differential Equations

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

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