Time-changed Ornstein–Uhlenbeck process

DOI10.1088/1751-8113/48/13/135004zbMath1309.82025OpenAlexW2039290222MaRDI QIDQ5246127

Janusz Gajda, Agnieszka Wyłomańska

Publication date: 17 April 2015

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/1751-8113/48/13/135004

zbMATH Keywords

subordinationOrnstein-Uhlenbeck processcovariancefractional Fokker-Planck equation

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) Analysis of variance and covariance (ANOVA) (62J10) Fractional partial differential equations (35R11) Fokker-Planck equations (35Q84)

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Non-local solvable birth-death processes ⋮ Tempered relaxation equation and related generalized stable processes ⋮ First passage times for some classes of fractional time-changed diffusions ⋮ Least squares estimator for a class of subdiffusion processes ⋮ The Fokker–Planck equation for the time-changed fractional Ornstein–Uhlenbeck stochastic process ⋮ Explicit representation of characteristic function of tempered α‐stable Ornstein–Uhlenbeck process ⋮ Time-changed fractional Ornstein-Uhlenbeck process ⋮ Ornstein-Uhlenbeck process driven by \(\alpha\)-stable process and its gamma subordination ⋮ Commutative and associative properties of the Caputo fractional derivative and its generalizing convolution operator ⋮ Tempered fractional Langevin–Brownian motion with inverse β-stable subordinator ⋮ Long-memory Gaussian processes governed by generalized Fokker-Planck equations ⋮ Convergence results for the time-changed fractional Ornstein–Uhlenbeck processes ⋮ Fractional immigration-death processes ⋮ Time-non-local Pearson diffusions ⋮ Modeling anomalous diffusion by a subordinated integrated Brownian motion

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