105 citations · 151 across the 9 of their papers we have counts for
4 papers · 1 filter
Approximation Operators, Exponential, q-Exponential, and Free Exponential Families
Wlodzimierz Bryc, Mourad Ismail
Using the technique developed in approximation theory, we construct examples of exponential families of infinitely divisible laws which can be viewed as deformations of the normal,…
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…