Quantum Stochastic Processes and Noncommutative Geometry

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The classical theory of stochastic processes has important applications arising from the need to describe irreversible evolutions in classical mechanics; analogously quantum stochastic processes can be used to model the dynamics of irreversible quantum systems. Noncommutative, i.e. quantum, geometry provides a framework in which quantum stochastic structures can be explored. This book is the first to describe how these two mathematical constructions are related. In particular, key ideas of semigroups and complete positivity are combined to yield quantum dynamical semigroups (QDS). Sinha and Goswami also develop a general theory of Evans-Hudson dilation for both bounded and unbounded coefficients. The unique features of the book, including the interaction of QDS and quantum stochastic calculus with noncommutative geometry and a thorough discussion of this calculus with unbounded coefficients, will make it of interest to graduate students and researchers in functional analysis, probability and mathematical physics.

Probability and Stochastic Processes (4版)

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【簡介】 Probability and Stochastic Processes – A Friendly Introduction for Electrical and Computer Engineers, Fourth Edition serves as an accessible guide for engineering students delving into the realms of probability theory and stochastic processes.This text strikes a balance between rigorous mathematical exposition and clear, intuitive explanations, ensuring that students grasp the fundamental concepts essential for applying mathematics to real-world engineering challenges. Enhanced with the practical MATLAB applications. The book offers students valuable hands-on experienceto reinforce the theoretical material. This International adaptation has been thoroughly revised and updated. Notably, it includes a new chapter on Probabilistic Inequalities and Bounds. The sections on Stochastic Processes and Sums of Random Variables have been comprehensively enhanced to encompass additional topics, aligning with the latest curriculum requirements. With an array of new and updated examples, quizzes, and end-of-chapter problems, the book provides robust support to students, particularly in bridging the gap between theoretical probability and its practical applications in engineering. 【目錄】 1 Random Experiments, Models, and Probabilities 2 Sequential Random Experiments 3 Discrete Random Variables 4 Continuous Random Variables 5 Multiple Random Variables 6 Probability Models of Derived Random Variables 7 Conditional Probability Models 8 Random Vectors 9 Sums of Random Variables 10 Hypothesis Testing 11 Estimation of a Random Variable 12 Some Probabilistic Inequalities and Bounds 13 Stochastic Processes and Markov Chains 14 Stationary Processes and Random Signal Processing Appendix A The Sample Mean Appendix B Families of Random Variables Appendix C A Few Math Facts