Title: Markov Processes With Linear Regressions and Quadratic Conditional Variances
Speaker: Wlodzimierz Bryc (University of Cincinnati)
Abstract: This talks is about “quadratic harnesses,” which are Markov processes with linear regressions and quadratic conditional variances under the two-sided conditioning. Such processes generically have polynomial conditional moments, and the transition probabilities are uniquely determined by the orthogonal martingale polynomials. Examples include Lévy-Meixner processes, Markov processes that come from the q-Brownian motion and “free Levy processes” from the non-commutative probability, and some other less familiar processes.