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Large deviations, stochastic control and stochastic numerical methods

Pierre Nyquist
(Department of Mathematics, KTH Royal Institute of Technology, Stockholm)
Monday, 16 January, 2017, at 11:15-12:00, in Aud. D1 (1531-113)
Large deviations theory and stochastic numerical methods, often referred to as Monte Carlo methods, are two of the preeminent branches of applied probability. The former is the part of probability theory which characterizes rare events, whereas the latter is playing an increasingly important role in, for example, statistical inference, engineering and the physical sciences, where complex stochastic models often render exact analyses intractable.

In this talk, I will discuss the interplay between large deviations and (advanced) Monte Carlo methods, involving also topics such as stochastic optimal control, calculus of variations, PDE theory and optimization. After an introductory part, I will focus on some specific examples, illustrating the use of tools form large deviations and related areas in understanding various aspects of stochastic numerical methods. In particular, I will discuss a novel use of empirical measures to analyze the stochastic processes underlying simulation schemes. Time permitting I will close with a brief discussion of some related on-going activities, concerning for example statistical learning and stochastic optimization.

The talk will be completely self-contained, assuming no prior knowledge of large deviations, stochastic control or advanced Monte Carlo methodology.
Contact person: Niels O. Nygaard