105 citations · 151 across the 9 of their papers we have counts for
3 papers · 2 filters
The bi-Poisson process: a quadratic harness
Włodzimierz Bryc, Wojciech Matysiak, Jacek Wesołowski
This paper is a continuation of our previous research on quadratic harnesses, that is, processes with linear regressions and quadratic conditional variances. Our main result is a c…
Classical bi-Poisson process: an invertible quadratic harness
Wlodzimierz Bryc, Jacek Wesolowski
We give an elementary construction of a time-invertible Markov process which is discrete except at one instance. The process is one of the quadratic harnesses studied in our previo…
Quadratic Harnesses, q-commutations, and orthogonal martingale polynomials
Wlodzimierz Bryc, Wojciech Matysiak, Jacek Wesolowski
We introduce the quadratic harness condition and show that integrable quadratic harnesses have orthogonal martingale polynomials with a three step recurrence that satisfies a q-com…