Martingales from pairs of randomized Poisson, Gamma, neg binomial and hyperbolic secant processes

Опубликовано 15 июля 2016, 18:35

Martingales from pairs of randomized Poisson, Gamma, negative binomial and hyperbolic secant processes
4:20 - 5:00 Wlodzimierz Bryc (U Cincinnati) Martingales from pairs of randomized Poisson, Gamma, negative binomial and hyperbolic secant processes
Abstract: Consider a pair of independent Poisson processes, or a pair of Negative Binomial processes, or Gamma, or hyperbolic secant processes with a shared randomly selected parameter. Under appropriate randomization, one can deterministically re-parametrize the time and scale for both processes so that the first process runs on time interval $(0,1)$, the second process runs on time interval $(1,\infty)$, and the two processes seamlessly join into one Markov martingale on $(0,\infty)$. In fact, a property stronger than martingale holds: we stitch together two processes into a single quadratic harness on $(0,\infty)$. This talk is based on joint work in progress with J. Wesolowski.