Bilateral birth and death process in q-calculus

DOI10.1080/17442508.2022.2055967zbMath1524.60190arXiv2106.14283OpenAlexW4221026721WikidataQ114010498 ScholiaQ114010498MaRDI QIDQ6107676

Lazhar Dhaouadi

Publication date: 3 July 2023

Published in: Stochastics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2106.14283

zbMATH Keywords

\(q\)-Hankel transform\(q\)-Bessel functionbilateral birth and death process

Mathematics Subject Classification ID

Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10)

Cites Work

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• Positivity of the generalized translation associated with the \(q\)-Hankel transform
• Some basic Lommel polynomials
• Quantum extensions of semigroups generated by Bessel processes
• The Classification of Birth and Death Processes
• Exactly solvable birth and death processes
• On q-Analogues of the Fourier and Hankel Transforms
• An Addition Theorem and Some Product Formulas for the Hahn-Exton q-Bessel Functions
• Classical and Quantum Markov Processes Associated with q-Bessel Operators
• On the $q$-Bessel Fourier transform
• Positivity of the generalized translation associated with theq-Hankel transform and applications
• Bilateral Birth and Death Processes

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