Approximation of stationary solutions to SDEs driven by multiplicative fractional noise

2012/11/20 by Serge Cohen, Cohen, Serge, Fabien Panloup +3
Economics, Econometrics and Finance · #Complex Systems and Time Series Analysis #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and financial applications

paper · doi:10.48550/arxiv.1211.4813

openalex publication_date 2012/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Fractional Brownian Motions, Fractional Noises and Applications

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