Some Processes Associated with Fractional Bessel Processes期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

Some Processes Associated with Fractional Bessel Processes

Authors:	Email author" target="_blank">Y?Hu Email author D?Nualart

Institution:	(1) Department of Mathematics, University of Kansas, 405 Snow Hall, Lawrence, KS 66045-2142, USA;(2) Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain

Abstract:	Let $B = { (B_t^{1}, ..., B_t^{d} ),t \geq 0}$ be a d-dimensional fractional Brownian motion with Hurst parameter H and let $R_{t} = \sqrt {(B_t^1 )^2 + ... + (B_t^{d} )^{2} }$ be the fractional Bessel process. Itôs formula for the fractional Brownian motion leads to the equation $R_t = \sum_{i = 1}^d ,\int_0^{t} \frac{B_s^{i} }{R_{s} }\ {d} B_s^i + H(d -1)\int_0^{t} \frac{s^{2H - 1}} {R_s }\ {d} s$ . In the Brownian motion case $(H=1/2), X_t = \sum\nolimits_{i = 1}^d {\int_0^t {\frac{{B_s^i }} {{R_s }}} } \d B_s^i$ is a Brownian motion. In this paper it is shown that X_t is not an ${\cal F}^{B}$ -fractional Brownian motion if H 1/2. We will study some other properties of this stochastic process as well.

Keywords:	Fractional Brownian motion fractional Bessel processes stochastic integral Malliavin derivative chaos expansion
本文献已被 SpringerLink 等数据库收录！