We develop a new algorithm for the estimation of rare event probabilities associated with the steady-state of a Markov stochastic process with continuous state space Rd and discrete time steps (i.e., a discrete-time Rd-valued Markov chain). The algorithm, which we coin Recurrent Multilevel Splitting (RMS), relies on the Markov chain's underlying recurrent structure, in combination with the Multilevel Splitting method. Extensive simulation experiments are performed, including experiments with a nonlinear stochastic model that has some characteristics of complex climate models. The numerical experiments show that RMS can boost the computational efficiency by several orders of magnitude compared to the Monte Carlo method.
Rare Event Sampling Methods: Development, Analysis and Application, Markov processes, Computational methods, Stochastic processes, Monte Carlo methods, Probability theory, Data science, Operations research
CHAOS, An Interdisciplinary Journal of Nonlinear Science
Centrum Wiskunde & Informatica, Amsterdam, The Netherlands

Bisewski, K.L, Crommelin, D.T, & Mandjes, M.R.H. (2019). Rare event simulation for steady-state probabilities via recurrency cycles. CHAOS, An Interdisciplinary Journal of Nonlinear Science, 29(3). doi:10.1063/1.5080296