Geodesic
Kolmogorov equation and large-time behaviour for fractional Brownian motion driven linear SDE's
Applications of Mathematics, Tome 50 (2005) no. 1, pp. 63-81.

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We consider a stochastic process Xtx 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 Φ are real matrices and BH is a fractional Brownian motion with Hurst parameter H∈(1/2,1). The Kolmogorov backward equation for the function u(t,x)=Ef(Xtx) is derived and exponential convergence of probability distributions of solutions to the limit measure is established.
DOI : 10.1007/s10492-005-0004-4
Classification : 60G15, 60H05, 60H10
Mots-clés : fractional Brownian motion; Kolmogorov backwards equation; linear stochastic equation 
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Vyoral, Michal. Kolmogorov equation and large-time behaviour for fractional Brownian motion driven linear SDE's. Applications of Mathematics, Tome 50 (2005) no. 1, pp. 63-81. doi : 10.1007/s10492-005-0004-4. https://geodesic-test.mathdoc.fr/articles/10.1007/s10492-005-0004-4/

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