# Stochastic approximation of quasi-stationary distributions for diffusion processes in a bounded domain

## TL;DR

This paper introduces a stochastic approximation method to estimate the quasi-stationary distribution of diffusion processes in bounded domains, demonstrating convergence of the occupation measure to the distribution.

## Contribution

It presents a novel stochastic approximation approach for quasi-stationary distributions of diffusions, combining recent theoretical results with reinforcement-based processes.

## Key findings

- Occupation measure converges to the unique quasi-stationary distribution.
- Method effectively estimates quasi-stationary distributions in bounded domains.
- Theoretical proofs confirm convergence using stochastic approximation techniques.

## Abstract

We study a random process with reinforcement, which evolves following the dynamics of a given diffusion process in a bounded domain and is resampled according to its occupation measure when it reaches the boundary. We show that its occupation measure converges to the unique quasi-stationary distribution of the diffusion process absorbed at the boundary of the domain. Our proofs use recent results in the theory of quasi-stationary distributions and stochastic approximation techniques.