Derivative for self-intersection local time of multidimensional fractional Brownian motion

作者：Yan, Litan^*; Yu, Xianye

来源：Stochastics-An International Journal of Probability and Stochastic Reports, 2015, 87(6): 966-999.

DOI：10.1080/17442508.2015.1019883

• fractional Brownian motion
• self-intersection local time
• occupation formula
• Chaos expansion
• quadratic covariation

Let B-H be a fractional Brownian motion taking values in R-N with Hurst index 0 < H < 1. In this paper, we consider the self-intersection local time beta(t)(a) and its derivative in the spatial variable a is an element of R-N. In particular, we introduce the so-called integrated quadratic covariation left perpendicularf(B-H), B(H)right perpendicular((IC)) and show that the Bouleau-Yor type identity
[f(B-H), B-H](t)((IC)) = -Sigma(N)(j=1) integral(RN) (partial derivative/partial derivative a(j)beta(t)(a)f(a)da(1)da(2)...da(N)
holds for some suitable f.

• 出版日期2015
• 单位东华大学