## Bernoulli

• Bernoulli
• Volume 8, Number 3 (2002), 367-405.

### Recursive computation of the invariant distribution of a diffusion

#### Abstract

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.

#### Article information

Source
Bernoulli, Volume 8, Number 3 (2002), 367-405.

Dates
First available in Project Euclid: 8 March 2004

https://projecteuclid.org/euclid.bj/1078779875

Mathematical Reviews number (MathSciNet)
MR2004b:60193

Zentralblatt MATH identifier
1006.60074

#### Citation

Lamberton, Damien; Pagès, Gilles. Recursive computation of the invariant distribution of a diffusion. Bernoulli 8 (2002), no. 3, 367--405. https://projecteuclid.org/euclid.bj/1078779875

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