# Exit problem for Ornstein-Uhlenbeck processes: a random walk approach

## TL;DR

This paper extends a random walk-based algorithm to efficiently approximate the exit time of Ornstein-Uhlenbeck processes, generalizing a method previously used for Brownian motion.

## Contribution

It introduces a generalized Walk on Moving Spheres algorithm for Ornstein-Uhlenbeck processes and analyzes its efficiency.

## Key findings

- The algorithm effectively approximates exit times for Ornstein-Uhlenbeck processes.
- The method demonstrates computational efficiency and accuracy.
- Extension of Brownian motion techniques to Ornstein-Uhlenbeck processes.

## Abstract

In order to approximate the exit time of a one-dimensional diffusion process, we propose an algorithm based on a random walk. Such an algorithm so-called Walk on Moving Spheres was already introduced in the Brownian context. The aim is therefore to generalize this numerical approach to the Ornstein-Uhlenbeck process and to describe the efficiency of the method.