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Probability and Computational Finance Seminar
Ramon van Handel ORFE Princeton Title: An asymptotic theory for nonlinear filters Abstract: The theory of nonlinear filtering is concerned with the conditional law of a Markov process (the signal) given a sequence of noisy observations. A collection of recent results gives new insight into the long time asymptotic properties of nonlinear filters. On the one hand, ergodicity of the filter is inherited from ergodicity of the signal, largely resolving a long-standing gap in a classic paper by H. Kunita (1971). On the other hand, certain structural properties of filtering models, reminiscent of fundamental ideas in systems theory, ensure stability of the filter in the absence of ergodicity. Key to the proofs are martingale arguments and the ergodic theory of Markov chains in random environments. If time permits, I will outline applications to the convergence of Monte Carlo particle filtering algorithms, to the asymptotics of the stationary estimation error, and to the pathwise optimality of decisions under partial information. Date: Monday, April 19, 2010 Time: 5:00 pm Location: Wean Hall 6423 |