Functional Distribution of Anomalous and Nonergodic Diffusion: From Stochastic Processes to Pdes (Hardcover) (ISBN-13: 9789811250491)

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騅y process, L騅y 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.

Author: Weihua Deng, Xudong Wang, Daxin Nie
ISBN-10: 9811250499
ISBN-13: 9789811250491
Publisher: World Scientific Publishing Company
Language: English
Published: 07/08/2022
Pages: 260
Format: Hardcover
Weight: 1.13lbs
Size: 9.00h x 6.00w x 0.63d