Rare Event Simulation for the Stationary Distribution of a Markov Chain

Krzysztof Bisewski
(CWI, Amsterdam)
Stochastics Seminar
Thursday, 29 November, 2018, at 13:15-14:00, in Koll. D (1531-211)
Abstract:
I will present a new algorithm for the estimation of small probabilities associated with the steady-state of a Markov stochastic process with continuous state space $R^d$ and discrete time steps (i.e. a discrete-time $R^d$-valued Markov chain). A notable class of such processes are numerical solution to a Stochastic Differential Equations. The algorithm, which we coin Recurrent Multilevel Splitting (RMS), relies on the Markov chain’s underlying recurrent structure (similar to the regenerative property), in combination with the Multilevel Splitting method. The numerical experiments show that RMS can boost the computational efficiency by several orders of magnitude compared to the standard Monte Carlo method.


Contact person: Jevgenijs Ivanovs