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Title: Kolmogorov equation and large-time behaviour for fractional Brownian motion driven linear SDE's (English)
Author: Vyoral, Michal
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940 (print)
ISSN: 1572-9109 (online)
Volume: 50
Issue: 1
Year: 2005
Pages: 63-81
Summary lang: English
Category: math
Summary: We consider a stochastic process $X_t^x$ which solves an equation \[ {\mathrm d}X_t^x = AX_t^x\mathrm{d}t + \Phi {\mathrm d}B^H_t,\quad X_0^x = x \] where $A$ and $\Phi $ are real matrices and $B^H$ is a fractional Brownian motion with Hurst parameter $H \in (1/2,1)$. The Kolmogorov backward equation for the function $u(t,x) = \mathbb{E} f(X^x_t)$ is derived and exponential convergence of probability distributions of solutions to the limit measure is established. (English)
Keyword: fractional Brownian motion
Keyword: Kolmogorov backwards equation
Keyword: linear stochastic equation
MSC: 60G15
MSC: 60H05
MSC: 60H10
idZBL: Zbl 1099.60040
idMR: MR2117696
DOI: 10.1007/s10492-005-0004-4
Date available: 2009-09-22T18:20:32Z
Last updated: 2020-07-02
Stable URL:
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