Small-time kernel expansion for solutions of stochastic differential equations driven by fractional Brownian motions

被引：17

作者：

Baudoin, Fabrice ^{[1
]}

Ouyang, Cheng ^{[1
]}

机构：

[1] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2011年 / 121卷 / 04期

基金：

美国国家科学基金会;

关键词：

Fractional Brownian motion; Small times expansion; Laplace method; Stochastic differential equation; ASYMPTOTIC DEVELOPMENT; INTEGRATION; CALCULUS;

D O I：

10.1016/j.spa.2010.11.011

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

The goal of this paper is to show that under some assumptions, for a d-dimensional fractional Brownian motion with Hurst parameter H > 1/2, the density of the solution of the stochastic differential equation X(t)(x) = x + Sigma(d)(i = 1) integral(t)(0) V(i)(X(s)(x))dB(s)(i), admits the following asymptotics at small times: p(t; x, y) = 1/(t(H))(d)e(-d2(x, y)/2t2H)(Sigma(N)(i=0)ci(x, y)t(2iH) + O(t(2(N+1)H))). (C) 2010 Elsevier B.V. All rights reserved.

引用

页码：759 / 792

页数：34

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