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.
Contents:
- Probability Theory
- Anomalous and Nonergodic Diffusion
- Functional Distributions
- Algorithms for the Models Governing Functional Distribution
- Appendix A: Fractional Calculus and Related Spaces
Readership: Graduate and postgraduate students, as well as researchers in mathematics, physics and chemistry.
Key Features:
- Functionals of anomalous and nonergodic diffusions are topical issues where we treat them from both the practical physical applications and mathematical analyses/algorithms
- This volume clearly explains the physical motivation and provides the mathematical foundations
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