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Approximation of stationary solutions to SDEs driven by multiplicative fractional noise. (English) Zbl 1285.60068

Summary: In a previous paper, we studied the ergodic properties of an Euler scheme of a stochastic differential equation with a Gaussian additive noise in order to approximate the stationary regime of such an equation. We now consider the case of multiplicative noise when the Gaussian process is a fractional Brownian motion with Hurst parameter \(H>1/2\) and obtain some (functional) convergence properties of some empirical measures of the Euler scheme to the stationary solutions of such SDEs.

MSC:

60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
60G10 Stationary stochastic processes
60G15 Gaussian processes

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