Random walk with long-range interaction with a barrier and its dual: exact results

DOI10.1016/j.cam.2009.10.028zbMath1185.60082OpenAlexW1981841340MaRDI QIDQ847224

Thierry E. Huillet

Publication date: 12 February 2010

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2009.10.028

zbMATH Keywords

orthogonal polynomialslong-range interactionrandom interfacesbirth and death random walkwall duality

Mathematics Subject Classification ID

Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05)

Related Items (2)

Excursions and path functionals for stochastic processes with asymptotically zero drifts ⋮ Random walk weakly attracted to a wall

Cites Work

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• Random walks
• Random walk weakly attracted to a wall
• The weight functions, generating functions and miscellaneous properties of the sequences of orthogonal polynomials of the second kind associated with the Jacobi and the Gegenbauer polynomials
• Connection relations and bilinear formulas for the classical orthogonal polynomials
• Wall and Siegmund duality relations for birth and death chains with reflecting barrier
• A survey and some generalizations of Bessel processes
• On rare and extreme events
• First return probabilities of birth and death chains and associated orthogonal polynomials
• Singularity Analysis of Generating Functions
• Explicit Formulas for the Associated Jacobi Polynomials and Some Applications
• Spherically symmetric random walks in noninteger dimension
• The formal theory of birth-and-death processes, lattice path combinatorics and continued fractions

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