Orthogonal Polynomials in the Spectral Analysis of Markov Processes

DOI10.1017/9781009030540OpenAlexW3161136830MaRDI QIDQ5155136

Manuel D. De La Iglesia

Publication date: 6 October 2021

Full work available at URL: https://doi.org/10.1017/9781009030540

zbMATH Keywords

Laplace transformMarkov chainsrandom walksBrownian motionMarkov processesclassical orthogonal polynomialsdiffusion processesbirth-death processesAskey schemeFavard's theoremcontinuous Hahnbirth-death chainscontinuous Dual HahnDerman-Vere-Jones transformationKarlin-McGregor integral representationStiletjes transformUpadhyaya transform

Mathematics Subject Classification ID

Computational methods in Markov chains (60J22) Continuous-time Markov processes on general state spaces (60J25) Discrete-time Markov processes on general state spaces (60J05) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to probability theory (60-01) Brownian motion (60J65) Population dynamics (general) (92D25) Markov semigroups and applications to diffusion processes (47D07) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) (60J20) Numerical analysis or methods applied to Markov chains (65C40) Diffusion processes (60J60) Laplace transform (44A10) Moment problems (44A60) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) (60J70) Transition functions, generators and resolvents (60J35) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to special functions (33-01) Applications of continuous-time Markov processes on discrete state spaces (60J28)

Related Items (7)

Exactly solvable discrete time birth and death processes ⋮ Spectral analysis of bilateral birth–death processes: some new explicit examples ⋮ An urn model for the Jacobi-Piñeiro polynomials ⋮ QBD processes associated with Jacobi-Koornwinder bivariate polynomials and urn models ⋮ The bilateral birth–death chain generated by the associated Jacobi polynomials ⋮ Quantum Markov chains on the line: matrix orthogonal polynomials, spectral measures and their statistics ⋮ Birth-death chains on a spider: spectral analysis and reflecting-absorbing factorization

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