Approximation of stationary solutions to SDEs driven by multiplicative fractional noise

Serge Cohen (1) , Fabien Panloup (1) , Samy Tindel (2, 3)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 BIGS - Biology, genetics and statistics
3 IECL - Institut Élie Cartan de Lorraine

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.

Mots clés: Euler scheme; stationary process; fractional Brownian motion; stochastic differential equation

Domaines: Probabilités [math.PR]

Serge Cohen, Fabien Panloup, Samy Tindel. Approximation of stationary solutions to SDEs driven by multiplicative fractional noise. Stochastic Processes and their Applications, 2014, 124 (3), pp.1197-1225. ⟨10.1016/j.spa.2013.11.004⟩. ⟨hal-00754368v2⟩