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Kolmogorov equation and large-time behaviour for fractional brownian motion driven linear sde’s

Author： Vyroai Michal

Publisher： Springer Publishing Company

ISSN： 0862-7940

Source： Applications of Mathematics, Vol.50, Iss.1, 2005-02, pp. : 63-81

Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.

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Abstract

We consider a stochastic process X _t^x which solves an equation $$dX_t^x = AX_t^x dt + \Phi dB_t^H \quad X_0^x = x$$ where A and Φ are real matrices and B^H is a fractional Brownian motion with Hurst parameter H ∈ (1/2,1). The Kolmogorov backward equation for the function u(t,x) = $$H \in \left( {{1 \mathord{\left/ {\vphantom {1 {2,1}}} \right. \kern-\nulldelimiterspace} {2,1}}} \right)$$ f(X _t^x ) is derived and exponential convergence of probability distributions of solutions to the limit measure is established.

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