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Approximation of stationary solutions to SDEs driven by multiplicative fractional noise

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  • Cohen, Serge
  • Panloup, Fabien
  • Tindel, Samy

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.

Suggested Citation

  • Cohen, Serge & Panloup, Fabien & Tindel, Samy, 2014. "Approximation of stationary solutions to SDEs driven by multiplicative fractional noise," Stochastic Processes and their Applications, Elsevier, vol. 124(3), pages 1197-1225.
    • Handle: RePEc:eee:spapps:v:124:y:2014:i:3:p:1197-1225
    DOI: 10.1016/j.spa.2013.11.004
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    References listed on IDEAS

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    1. Lemaire, Vincent, 2007. "An adaptive scheme for the approximation of dissipative systems," Stochastic Processes and their Applications, Elsevier, vol. 117(10), pages 1491-1518, October.
    2. Paolo Guasoni, 2006. "No Arbitrage Under Transaction Costs, With Fractional Brownian Motion And Beyond," Mathematical Finance, Wiley Blackwell, vol. 16(3), pages 569-582, July.
    3. Gilles Pag`es & Fabien Panloup, 2007. "Approximation of the distribution of a stationary Markov process with application to option pricing," Papers 0704.0335, arXiv.org, revised Sep 2009.
    4. Cohen, Serge & Panloup, Fabien, 2011. "Approximation of stationary solutions of Gaussian driven stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 121(12), pages 2776-2801.
    5. Crauel, Hans, 1993. "Non-Markovian invariant measures are hyperbolic," Stochastic Processes and their Applications, Elsevier, vol. 45(1), pages 13-28, March.
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