$q$-Wiener and $(\alpha,q)$-Ornstein--Uhlenbeck Processes. A Generalization of Known Processes

DOI10.1137/S0040585X97985674zbMath1276.60045arXivmath/0507303MaRDI QIDQ4907611

Paweł Jerzy Szabłowski

Publication date: 4 February 2013

Published in: Theory of Probability & Its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0507303

zbMATH Keywords

strong Markov property\((\alpha,q)\)-Ornstein-Uhlenbeck process\(q\)-Wiener process

Mathematics Subject Classification ID

Special processes (60K99) Generalized stochastic processes (60G20) Stochastic processes (60G99)

Related Items (8)

On Markov processes with polynomial conditional moments ⋮ Large jumps of \(q\)-Ornstein-Uhlenbeck processes ⋮ On the families of polynomials forming a part of the Askey–Wilson scheme and their probabilistic applications ⋮ Extremes of \(q\)-Ornstein-Uhlenbeck processes ⋮ Markov processes, polynomial martingales and orthogonal polynomials ⋮ On the generalized Kesten–McKay distributions ⋮ Moments of \(q\)-normal and conditional \(q\)-normal distributions ⋮ On integration with respect to the \(q\)-Brownian motion

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