# Rare Event Simulation for the Stationary Distribution of a Markov Chain

## Seminar/Forum

101
Peter Hall
In this talk I will present a new algorithm for the estimation of small probabilities associated with the steady-state of a discrete-time $R^d$-valued Markov chain. A notable class of such processes are numerical solutions to Stochastic Differential Equations. The algorithm, which we coin Recurrent Multilevel Splitting (RMS), relies on the Markov chain’s underlying recurrent structure (a concept akin to regeneration) in combination with the Multilevel Splitting method (a well known method for simulation of rare events). The numerical experiments show that RMS can boost the computational efficiency by several orders of magnitude compared to the standard Monte Carlo method.