Modeling Anomalous Diffusion

Modeling Anomalous Diffusion

From Statistics to Mathematics

Weihua Deng, Ru Hou;Wanli Wang;Pengbo Xu


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This book focuses on modeling the anomalous diffusion phenomena, being ubiquitous in the natural world. Both the microscopic models (stochastic processes) and macroscopic models (partial differential equations) have been built up. The relationships between the two kinds of models are clarified, and based on these models, some statistical observables are analyzed. From statistics to mathematics, the built models show their power with their associated applications.

This book is important for students to develop basic skills to be able to succeed in their future research. In addition to introducing the related models or methods, it also provides the corresponding applications and simulation results, which will attract more readers ranging from mathematicians to physicists or chemists, to name a few.

  • Stochastic Models
  • Fokker-Planck Equations
  • Feynman-Kac Equations
  • Aging Fokker-Planck and Feynman-Kac Equations
  • Fokker-Planck and Feynman-Kac Equations with Multiple Internal States
  • Fractional Reaction Diffusion Equations and Corresponding Feynman-Kac Equations
  • Renewal Theory for Fractional Poisson Process: Typical versus Rare
  • Governing Equation for Average First Passage Time and Transitions among Anomalous Diffusions

Readership: Advanced undergraduate and graduate students, and researchers in mathematics, physics, chenistry, amongst others, who are interested in the anomalous diffussion phenomena.Anomalous Diffusion;Modeling;Subordinated Processes;Feynman–Kac Equation0Key Features:
  • One of the authors, Weihua Deng, has an interdisciplinary research background with a deep understanding on the related anomalous models from the viewpoint of mathematics and physics
  • In this book, we not only introduce the widely investigated models but also discuss some new topics, for example, infinite densities, functionals, etc.
  • This book will get more attention from undergraduates and some high-level students