On a \(q\)-steady state Markov chain model based on transformed dual \(q\)-Krawtchouk orthogonal polynomials and its limiting behaviour

DOI10.1007/s11009-009-9148-0zbMath1206.60069OpenAlexW2057971944MaRDI QIDQ607611

Malvina G. Vamvakari, Andreas George Kyriakoussis

Publication date: 22 November 2010

Published in: Methodology and Computing in Applied Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11009-009-9148-0

zbMATH Keywords

Markov chain\texttt{MAPLE}\(q\)-continuous Gauss distribution\(q\)-discrete distribution\(q\)-Hermite distributiondual \(q\)-Krawtchouk orthogonal polynomials

Mathematics Subject Classification ID

Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Computation of special functions and constants, construction of tables (65D20) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80) Other special orthogonal polynomials and functions (33C47)

Related Items (2)

A \(q\)-analogue of the Stirling formula and a continuous limiting behaviour of the \(q\)-binomial distribution -- numerical calculations ⋮ \(q\)-discrete distributions based on \(q\)-Meixner and \(q\)-Charlier orthogonal polynomials-asymptotic behaviour

Uses Software

• Maple
• qseries

Cites Work

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• \(q\)-discrete distributions based on \(q\)-Meixner and \(q\)-Charlier orthogonal polynomials-asymptotic behaviour
• \(q\)-Gaussian processes: Non-commutative and classical aspects
• The moment problem associated with the Stieltjes-Wigert polynomials
• Moments of a class of discrete \(q\)-distributions
• Steady-state Markov chain models for certain \(q\)-confluent hypergeometric distributions
• Steady-state Markov chain models for the Heine and Euler distributions
• Absorption sampling and the absorption distribution
• A Method for q-Calculus
• Aq-deformed Poisson distribution based on orthogonal polynomials
• q-Probability: I. Basic Discrete Distributions
• The q-deformed binomial distribution and its asymptotic behaviour

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