105 citations · 144 across the 3 of their papers we have counts for
6 papers
On a class of free Levy laws related to a regression problem
Marek Bozejko, Wlodzimierz Bryc
The free Meixner laws arise as the distributions of orthogonal polynomials with constant-coefficient recursions. We show that these are the laws of the free pairs of random variabl…
Conditional moments of q-Meixner processes
Wlodzimierz Bryc, Jacek Wesolowski
We show that stochastic processes with linear conditional expectations and quadratic conditional variances are Markov, and their transition probabilities are related to a three-par…
Probabilistic aspects of Al-Salam-Chihara polynomials
Wlodzimierz Bryc, Wojciech Matysiak, Pawel J. Szablowski
We solve the connection coefficient problem between the Al-Salam-Chihara polynomials and the q-Hermite polynomials, and we use the resulting identity to answer a question from prob…
Large deviations of empirical measures under symmetric interaction
Wlodek Bryc
In this paper we study empirical measures which can be thought as a decoupled version of the empirical measures generated by random matrices. We prove the large deviation principle…
Stationary random fields with linear regressions
Wlodzimierz Bryc
We analyze certain stationary fields with linear regressions and quadratic conditional variances. This classic probabilistic problem leads somewhat unexpectedly to stationary Marko…
Stationary Markov chains with linear regressions
Wlodzimierz Bryc
In a previous paper we determined one dimensional distributions of a stationary field with linear regressions and quadratic conditional variances under a linear constraint on the c…