Functional Distribution of Anomalous and Nonergodic Diffusion: From Stochastic Processes to Pdes
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This volume presents a pedagogical review of the functional distribution of anomalous and nonergodic diffusion and its numerical simulations, starting from the studied stochastic processes to the deterministic partial differential equations governing the probability density function of the functionals. Since the remarkable theory of Brownian motion was proposed by Einstein in 1905, it had a sustained and broad impact on diverse fields, such as physics, chemistry, biology, economics, and mathematics. The functionals of Brownian motion are later widely attractive for their extensive applications. It was Kac, who firstly realized the statistical properties of these functionals can be studied by using Feynman's path integrals.In recent decades, anomalous and nonergodic diffusions which are non-Brownian become topical issues, such as fractional Brownian motion, L vy process, L vy walk, among others. This volume examines the statistical properties of the non-Brownian functionals, derives the governing equations of their distributions, and shows some algorithms for solving these equations numerically.
Format:Hardcover
Language:English
ISBN:9811250499
ISBN13:9789811250491
Release Date:June 2022
Publisher:World Scientific Publishing Company
Length:260 Pages
Weight:1.13 lbs.
Dimensions:0.6" x 6.0" x 9.0"
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