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Recursive computation of the invariant distributions of Feller processes: Revisited examples and new applications

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  • Pagès Gilles

    (Sorbonne Université, LPSM, UMR 8001, case 158, 4, Place Jussieu, 75275ParisCedex 5, France)

  • Rey Clément

    (École Polytechnique, CMAP, Route de Saclay, 91128Palaiseau, France)

Abstract

In this paper, we show that the abstract framework developed in [G. Pagès and C. Rey, Recursive computation of the invariant distribution of Markov and Feller processes, preprint 2017, https://arxiv.org/abs/1703.04557] and inspired by [D. Lamberton and G. Pagès, Recursive computation of the invariant distribution of a diffusion, Bernoulli 8 2002, 3, 367–405] can be used to build invariant distributions for Brownian diffusion processes using the Milstein scheme and for diffusion processes with censored jump using the Euler scheme. Both studies rely on a weakly mean-reverting setting for both cases. For the Milstein scheme we prove the convergence for test functions with polynomial (Wasserstein convergence) and exponential growth. For the Euler scheme of diffusion processes with censored jump we prove the convergence for test functions with polynomial growth.

Suggested Citation

  • Pagès Gilles & Rey Clément, 2019. "Recursive computation of the invariant distributions of Feller processes: Revisited examples and new applications," Monte Carlo Methods and Applications, De Gruyter, vol. 25(1), pages 1-36, March.
    • Handle: RePEc:bpj:mcmeap:v:25:y:2019:i:1:p:1-36:n:1
    DOI: 10.1515/mcma-2018-2027
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    References listed on IDEAS

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