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Recursive computation of invariant distributions of Feller processes

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  • Pagès, Gilles
  • Rey, Clément

Abstract

This paper provides a general and abstract approach to compute invariant distributions for Feller processes. More precisely, we show that the recursive algorithm presented in Lamberton and Pagès (2002) and based on simulation algorithms of stochastic schemes with decreasing steps can be used to build invariant measures for general Feller processes. We also propose various applications: Approximation of Markov Brownian diffusion stationary regimes with a Milstein or an Euler scheme and approximation of a Markov switching Brownian diffusion stationary regimes using an Euler scheme.

Suggested Citation

  • Pagès, Gilles & Rey, Clément, 2020. "Recursive computation of invariant distributions of Feller processes," Stochastic Processes and their Applications, Elsevier, vol. 130(1), pages 328-365.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:1:p:328-365
    DOI: 10.1016/j.spa.2019.03.008
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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. 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.
    3. Mei, Hongwei & Yin, George, 2015. "Convergence and convergence rates for approximating ergodic means of functions of solutions to stochastic differential equations with Markov switching," Stochastic Processes and their Applications, Elsevier, vol. 125(8), pages 3104-3125.
    4. Panloup, Fabien, 2008. "Computation of the invariant measure for a Lévy driven SDE: Rate of convergence," Stochastic Processes and their Applications, Elsevier, vol. 118(8), pages 1351-1384, August.
    5. Ganidis, H. & Roynette, B. & Simonot, F., 1999. "Convergence rate of some semi-groups to their invariant probability," Stochastic Processes and their Applications, Elsevier, vol. 79(2), pages 243-263, February.
    6. Basak, Gopal K. & Hu, Inchi & Wei, Ching-Zong, 1997. "Weak convergence of recursions," Stochastic Processes and their Applications, Elsevier, vol. 68(1), pages 65-82, May.
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    Cited by:

    1. Gilles Pagès & Clément Rey, 2023. "Discretization of the Ergodic Functional Central Limit Theorem," Journal of Theoretical Probability, Springer, vol. 36(1), pages 1-44, March.

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