TL;DR
This paper analyzes a specific non-homogeneous Markov process linked to free probability, providing an explicit generator expression without relying on free probability techniques.
Contribution
It offers a self-contained derivation of the generator for a free probability-inspired Markov process, expanding understanding of its dynamics.
Findings
Explicit generator expression for the transition operator
Process related to free probability and quadratic regressions
Self-contained derivation without free probability tools
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.
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