Defense for Nitsan Ben-Gal
Probability Seminar
Abstract: We study an approximation scheme for a nonlinear filtering problem when the (unobservable) state process {X(t)} is the solution of a stochastic delay diffusion equation, and the observation process {Y(t)} is a noisy function of the segment process, i.e. of X(s) for s in [t-r,t], where r is a constant. The rate of convergence of this scheme is computed when the approximating state is the piecewise linear Euler-Maruyama scheme, and the observation process is a noisy function of (the piecewise constant segment of) the approximating state. The proof is based on a general technique, which can be used also for other classes of partially observable systems, and on upper bounds (extending previously known ones) for the moments of the modulus of continuity of an Ito process. Based on joint works with A. Calzolari, P. Florchinger, and M. Fischer.
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