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April 2002 Recursive computation of the invariant distribution of a diffusion
Damien Lamberton, Gilles Pagès
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Bernoulli 8(3): 367-405 (April 2002).


We propose a recursive stochastic algorithm with decreasing step to compute the invariant distribution $v$ of a Brownian diffusion process, in which we approximate $ν(f)$ for a wide class of possibly unbounded continuous functions $f$. We consider a somewhat general setting which includes cases where the diffusion may have several invariant distributions. Our main convergence result contains as a corollary the almost sure central limit theorem. Further, we investigate the weak rate of convergence of the algorithm. We show, in the class of polynomial steps$\gamma_n=n^{-\alpha}$, that it can be at most $n^{1/3}$ when the white noise has third moment zero and $n^{1/4}$ otherwise, where $n$ denotes the number of iterations of the algorithm.


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Damien Lamberton. Gilles Pagès. "Recursive computation of the invariant distribution of a diffusion." Bernoulli 8 (3) 367 - 405, April 2002.


Published: April 2002
First available in Project Euclid: 8 March 2004

zbMATH: 1006.60074
MathSciNet: MR2004B:60193

Keywords: Almost sure Central Limit Theorem , central limit theorem , diffusion process , Invariant distribution , numerical probability , Stochastic algorithm

Rights: Copyright © 2002 Bernoulli Society for Mathematical Statistics and Probability

Vol.8 • No. 3 • April 2002
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