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Approximation of stationary solutions to SDEs driven by multiplicative fractional noise (1211.4813v2)
Published 20 Nov 2012 in math.PR
Abstract: 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 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) convergences properties of some empirical measures of the Euler scheme to the stationary solutions of such SDEs.