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

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:121

Article

Baudoin, Fabrice¹  Ouyang, Cheng¹ 

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

关键词: Fractional Brownian motion;    Small times expansion;    Laplace method;    Stochastic differential equation;   

DOI  :  10.1016/j.spa.2010.11.011

来源: Elsevier

【 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.

【 授权许可】

Free