Stochastic processes in classical and quantum physics and engineering

TL;DR

This book provides a comprehensive overview of stochastic processes and their applications across classical and quantum physics, engineering, and biology, emphasizing theoretical foundations and practical problem-solving.

Contribution

It integrates stochastic calculus, large deviation theory, and quantum statistics to address diverse problems in physics, engineering, and biology, based on educational courses.

Findings

Application of stochastic processes to system identification and parameter estimation

Development of recursive algorithms for time series analysis in quantum systems

Analysis of stochastic methods in quantum information and fluid dynamics

Abstract

This book covers a wide range of problems involving the applications of stochastic processes, stochastic calculus, large deviation theory, group representation theory and quantum statistics to diverse fields in dynamical systems, electromagnetics, statistical signal processing, quantum information theory, quantum neural network theory, quantum filtering theory, quantum electrodynamics, quantum general relativity, string theory, problems in biology and classical and quantum fluid dynamics. The selection of the problems has been based on courses taught by the author to undergraduates and postgraduates in electronics and communication engineering. The theory of stochastic processes has been applied to problems of system identification based on time series models of the process concerned to derive time and order recursive parameter estimation followed by statistical performance analysis.