## Kolmogorov equation and large-time behaviour for fractional Brownian motion driven linear SDE’s.(English)Zbl 1099.60040

Summary: We consider a stochastic process $$X_t^x$$ which solves an equation $dX_t^x = AX_t^x\,dt + \Phi \,dB^H_t,\quad X_0^x=x,$ 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.

### MSC:

 60H05 Stochastic integrals 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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### References:

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