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

Pagès Gilles () and Rey Clément ()
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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

Monte Carlo Methods and Applications, 2019, vol. 25, issue 1, 1-36

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.

Keywords: Ergodic theory; Markov processes; invariant measures; limit theorem; stochastic approximation; Milstein scheme; censored jump processes (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1515/mcma-2018-2027

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