Markov processes with free Meixner laws
arXiv:0910.1061 · doi:10.1016/j.spa.2010.04.006
Abstract
We study a time-non-homogeneous Markov process which arose from free probability, and which also appeared in the study of stochastic processes with linear regressions and quadratic conditional variances. Our main result is the explicit expression for the generator of the (non-homogeneous) transition operator acting on functions that extend analytically to complex domain. The paper is self-contained and does not use free probability techniques.
References in corpus (6)
- On a class of free Levy laws related to a regression problem
- Conditional moments of q-Meixner processes
- Appell polynomials and their relatives
- Orthogonal polynomials with a resolvent-type generating function
- Free Meixner states
- Linearization coefficients for orthogonal polynomials using stochastic processes