Functional Distribution Of Anomalous And Nonergodic Diffusion: From Stochastic Processes To Pdes
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A01=Daxin Nie
A01=Weihua Deng
A01=Xudong Wang
Algorithm
Author_Daxin Nie
Author_Weihua Deng
Author_Xudong Wang
Category=PBKS
eq_isMigrated=1
eq_isMigrated=2
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Functional
Modelling
Partial Differential Equation
Probability Distribution
Regularity
Stochastic Process
Product details
- ISBN 9789811250491
- Publication Date: 08 Jul 2022
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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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, Lévy process, Lévy 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.
