Approximation of stationary solutions to SDEs driven by multiplicative fractional noise |
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Authors: | Serge Cohen Fabien Panloup Samy Tindel |
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Affiliation: | 1. Institut de Mathématiques de Toulouse (IMT) CNRS UMR 5219, Université Paul Sabatier (UPS) - Toulouse III–Université Toulouse le Mirail - Toulouse II–Université des Sciences Sociales - Toulouse I–Institut National des Sciences Appliquées (INSA), France;2. Institut Élie Cartan Lorraine, Université de Lorraine, B.P. 239, 54506 Vandœuvre-lès-Nancy Cedex, France |
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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 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. |
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Keywords: | 60G10 60G15 60H35 |
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