Rare Event Simulation Using Reversible Shaking Transformations

We introduce random transformations called reversible shaking transformations which we use to design two schemes for estimating rare event probability. One is based on interacting particle systems (IPS) and the other on time-average on a single path (POP) using ergodic theorem. We discuss their convergence rates and provide numerical experiments including continuous stochastic processes and jump processes. Our examples cover rather important situations related to insurance, queueing system and random graph for instance. Both schemes have good performance, with a seemingly better one for POP. Joint work with Gang LIU (Ecole Polytechnique).

Speaker Bio: E. Gobet graduated from Ecole Polytechnique, Paris and in 1998, he got a PhD degree in probability at University Paris Diderot. He took different positions at the University Pierre et Marie Curie, and the Grenoble Institute of Technology and he is currently a Professor in applied mathematics at Ecole Polytechnique. He is a specialist in stochastic processes, stochastic analysis, probabilistic algorithms, statistics for stochastic processes and financial mathematics. He has written more than 50 papers in international journals and 2 books.

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