The University of Arizona
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Girsanov theory and some applications in systems theory and physics

Event

Girsanov theory and some applications in systems theory and physics
Location: Online
Presenter: Maxim Raginsky, Electrical Engineering and Computing, University of Illinois, Urbana-Champaign

This talk is a guest lecture within the special topic Math 577 course on "Stochastic Control and Learning." by M. Chertkov

The change-of-measure theorem of Girsanov, extending earlier results of Cameron and Martin, is one of the fundamental results in stochastic calculus. It states that the absolute continuity of the probability law of one diffusion process with respect to another is equivalent to a transformation of drift. In this lecture, I will sketch the key ideas behind Girsanov's theorem and discuss its applications to several problems in systems theory (specifically, to filtering and to stochastic control of diffusion processes) and in mathematical physics (specifically, to a probabilistic Lagrangian interpretation of the Onsager-Machlup functional).