Distribution of Statistical Observables for Anomalous and Nonergodic Diffusions: From Statistics to Mathematics...

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Weihua Deng Xudong Wang

Distribution of Statistical Observables for Anomalous and Nonergodic Diffusions

From Statistics to Mathematics

Weihua Deng, Xudong Wang, Daxin Nie , Xing Liu

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English

CRC Press
27 May 2024

Stochastics; Classical mechanics; Electrical engineering

This book investigates statistical observables for anomalous and nonergodic dynamics, focusing on the dynamical behaviors of particles modelled by non-Brownian stochastic processes in the complex real-world environment.

Statistical observables are widely used for anomalous and nonergodic stochastic systems, thus serving as a key to uncover their dynamics. This study explores the cutting edge of anomalous and nonergodic diffusion from the perspectives of mathematics, computer science, statistical and biological physics, and chemistry. With this interdisciplinary approach, multiple physical applications and mathematical issues are discussed, including stochastic and deterministic modelling, analyses of (stochastic) partial differential equations (PDEs), scientific computations and stochastic analyses, etc. Through regularity analysis, numerical scheme design and numerical experiments, the book also derives the governing equations for the probability density function of statistical observables, linking stochastic processes with PDEs.

The book will appeal to both researchers of electrical engineering expert in the niche area of statistical observables and stochastic systems and scientists in a broad range of fields interested in anomalous diffusion, especially applied mathematicians and statistical physicists.

By: Weihua Deng, Xudong Wang, Daxin Nie, Xing Liu
Imprint: CRC Press
Country of Publication: United Kingdom
Dimensions: Height: 229mm, Width: 152mm,
Weight: 453g
ISBN: 9781032245232
ISBN 10: 1032245239
Pages: 227
Publication Date: 27 May 2024
Audience: College/higher education , Professional and scholarly , Primary , Undergraduate
Format: Paperback
Publisher's Status: Active

Weihua Deng is a professor of mathematics and statistical physics at Lanzhou University, China. His research interests include scientific computation and numerical analysis, statistical physics and stochastic simulations, nonlinear dynamics and anomalous diffusion, nonlocal PDE and stochastic representation, artificial intelligence and big data. Xudong Wang is a faculty member in the School of Science at Nanjing University of Science and Technology, China. His research focuses on stochastic processes, and stochastic modeling, as well as non-equilibrium statistical physics and his recent research interests include the theory and applications of normal and anomalous stochastic processes, and the stochastic models of intracellular transport. Daxin Nie is a research assistant in the School of Mathematics and Statistics at Lanzhou University, China. His research interests are numerical analyses for all kinds of anomalous diffusion equations. Xing Liu is a faculty member in the School of Mathematics and Economics at Hubei University of Education, China. He focuses on the research of the numerical methods and regularity of stochastic partial differential equation and his recent research interests include stochastic fractional diffusion equations and stochastic wave equation.