Free quadratic harness

DOI10.1016/j.spa.2010.11.013zbMath1226.60101arXiv1003.4771OpenAlexW1993010492MaRDI QIDQ550159

Jacek Wesołowski, Wojciech Matysiak, Wlodzimierz Bryc

Publication date: 8 July 2011

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1003.4771

zbMATH Keywords

hypergeometric orthogonal polynomialsharnessesquadratic conditional variancesfree Lévy processesorthogonal martingale polynomials

Mathematics Subject Classification ID

Continuous-time Markov processes on general state spaces (60J25) Noncommutative probability and statistics (46L53)

Related Items (5)

On Markov processes with polynomial conditional moments ⋮ Infinitesimal generators for a class of polynomial processes ⋮ Markov processes, polynomial martingales and orthogonal polynomials ⋮ A few remarks on quadratic harnesses ⋮ Dual Lukacs regressions for non-commutative variables

Cites Work

• Askey-Wilson polynomials, quadratic harnesses and martingales
• Conditional moments of \(q\)-Meixner processes
• Necessary and sufficient condition that the limit of Stieltjes transforms is a Stieltjes transform
• Semigroups of distributions with linear Jacobi parameters
• The bi-Poisson process: A quadratic harness
• Recurrence relations, continued fractions, and orthogonal polynomials
• Quadratic harnesses, $q$-commutations, and orthogonal martingale polynomials
• BI-POISSON PROCESS
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