Speaker: Alexey Kuznetsov
Title: Darboux transformation of diffusion processes
Abstract: Second-order linear differential operators can often be viewed as infinitesimal generators of diffusion processes and in this way they give rise to Markov semigroups of transition probability operators. We aim to investigate the Darboux transformation on the level of these diffusion processes and their Markov semigroups. We show that this transformation is closely related to Siegmund transform and Doob's h-transform of diffusion processes. The main application of Darboux transformation of diffusion processes is that it allows to construct new families of diffusions with explicitly computable transition probability densities. We will also discuss connections to exceptional orthogonal polynomials. This talk is based on joint work with Minjian Yuan.
Place: https://ucf.zoom.us/j/96789802247
Meeting ID: 967 8980 2247
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