Free Quadratic Harness
Wlodzimierz Bryc, Wojciech Matysiak, Jacek Weso{\l}owski
TL;DR
This paper provides a comprehensive, self-contained construction of the free quadratic harness, a Markov process with quadratic conditional variances, extending previous work limited to specific parameter ranges.
Contribution
It introduces a complete construction of the free quadratic harness applicable to all parameter values, expanding the theoretical understanding of quadratic harnesses.
Findings
Constructs the free quadratic harness for all parameters
Extends previous restricted parameter range results
Provides a self-contained framework for the process
Abstract
Free quadratic harness is a Markov process from the class of quadratic harnesses, i.e. processes with linear regressions and quadratic conditional variances. The process has recently been constructed for a restricted range of parameters in the paper "Askey-Wilson polynomials, quadratic harnesses and martingales" by W. Bryc and J. Weso{\l}owski using Askey--Wilson polynomials. Here we provide a self-contained construction of the free quadratic harness for all values of parameters.
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Taxonomy
TopicsRandom Matrices and Applications · Markov Chains and Monte Carlo Methods · Advanced Combinatorial Mathematics