Lamperti transformation of scaled Brownian motion and related Langevin equations

DOI10.1016/j.cnsns.2019.105077zbMath1453.82028OpenAlexW2981747205WikidataQ126978287 ScholiaQ126978287MaRDI QIDQ2207760

Marcin Magdziarz

Publication date: 23 October 2020

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cnsns.2019.105077

zbMATH Keywords

fractional Brownian motionLangevin equationanomalous diffusionstable Lévy motionergodicity breakingLamperti transformationscaled Brownian motion

Mathematics Subject Classification ID

Fractional processes, including fractional Brownian motion (60G22) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) Self-similar stochastic processes (60G18) Stochastic methods applied to problems in equilibrium statistical mechanics (82B31) Dynamical aspects of statistical mechanics (37A60)

Related Items (5)

Testing of fractional Brownian motion in a noisy environment ⋮ Extreme value statistics of positive recurrent centrally biased random walks ⋮ Spectral design of anomalous diffusion ⋮ Power Brownian motion ⋮ Discriminating Gaussian processes via quadratic form statistics

Cites Work

• The equivalence of ergodicity and weak mixing for infinitely divisible processes
• Ergodic properties of anomalous diffusion processes
• Ergodic properties of Lévy flights coexisting with subdiffusion and related models
• Discriminating between scaled and fractional Brownian motion via \(p\)-variation statistics
• Lamperti transformation -- cure for ergodicity breaking
• Aging and nonergodicity beyond the Khinchin theorem
• Analysis of short subdiffusive time series: scatter of the time-averaged mean-squared displacement
• Scale invariances and Lamperti transformations for stochastic processes
• Semi-Stable Stochastic Processes
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