Probability and Stochastic Processes for Physicists

This book aims to bridge the gap between probability and stochastic processes used by physicists and mathematicians, focusing on models and ideas. It covers probability spaces, random variables, limit theorems, stochastic processes, and Brownian motion, connecting the Schrödinger equation to diffusion processes.

Format: Paperback / softback
Length: 373 pages
Publication date: 26 June 2021
Publisher: Springer Nature Switzerland AG

This comprehensive book aims to bridge the gap between the language, models, and notations used by physicists and mathematicians when discussing probability and stochastic processes. The first four chapters provide a solid foundation by elucidating fundamental concepts such as probability spaces, measures, random variables, and limit theorems. While the focus is primarily on models and ideas, the discussion of limit theorems serves as a gateway to extensive coverage of the theory of stochastic processes. This includes topics such as stationarity and ergodicity, Poisson and Wiener processes, their trajectories, other Markov processes, jump-diffusion processes, stochastic calculus, and stochastic differential equations. These conceptual tools converge in a dynamical theory of Brownian motion, which compares the Einstein–Smoluchowski and Ornstein–Uhlenbeck approaches and highlights the key ideas that ultimately led to a connection between the Schrödinger equation and diffusion processes, following the lines of Nelsons stochastic mechanics.

A series of appendices provide detailed explanations and calculations, as well as concise treatments of thought-provoking topics. This book is an invaluable resource for students, researchers, and practitioners in the fields of physics, mathematics, and applied sciences, as it offers a comprehensive and accessible approach to probability and stochastic processes.

Weight: 593g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030484101
Edition number: 1st ed. 2020