Abstract: "In this thesis, we develop a mathematical formalism for the specification and proof of correctness of probabilistic communicating processes. This formalism combines a notion of probabilistic correctness with the theory of concurrency provided by the language of Communicating Sequential Processes (CSP). We first present the semantics of a model in which processes are defined as probability measures on the space of infinite traces. The model contains definitions for prefixing, probabilistic choice, hiding, simple parallel composition, sequential composition, interleaving, relabelling and recursion. These operators are defined as functions (mostly transformations) of probability measures.

This book discusses the semantic foundations of concurrent systems with nondeterministic and probabilistic behaviour. Particular attention is given to clarifying the relationship between testing and simulation semantics and characterising bisimulations from metric, logical, and algorithmic perspectives. Besides presenting recent research outcomes in probabilistic concurrency theory, the book exemplifies the use of many mathematical techniques to solve problems in computer science, which is intended to be accessible to postgraduate students in Computer Science and Mathematics. It can also be used by researchers and practitioners either for advanced study or for technical reference.

This volume, like the symposium CSP25 which gave rise to it, commemorates the semi-jubilee of Communicating Sequential Processes. 1 Tony Hoare’s paper “Communicating Sequential Processes” is today widely regarded as one of the most in?uential papers in computer science. To comm- orate it, an event was organized under the auspices of BCS-FACS (the British Computer Society’s Formal Aspects of Computing Science specialist group). CSP25 was one of a series of such events organized to highlight the use of formal methods, emphasize their relevance to modern computing and promote their wider application. BCS-FACS is proud that Tony Hoare presented his original ideas on CSP at one of its ?rst meetings, in 1978. The two-day event, 7–8 July 2004, was hosted by London South Bank U- versity’s Institute for Computing Research, Faculty of Business, Computing and Information Management. The intention was to celebrate, re?ect upon and look beyondthe?rstquarter-centuryofCSP’scontributionstocomputerscience. The meeting examined the impact of CSP on many areas stretching from semantics (mathematical models for understanding concurrency and communications) and logic(forreasoningaboutbehavior),throughthedesignofparallelprogramming languages (i/o, parallelism, synchronization and threads) to applications va- ing from distributed software and parallel computing to information security, Web services and concurrent hardware circuits. It included a panel discussion with panelists Brookes, Hoare, de Roever and Roscoe (chaired by Je? Sanders), poster presentations by PhD students and others, featured a ?re alarm (requ- ing evacuation in the rain!) and concluded with the presentation of a fountain pen to Prof. Sir C. A. R. Hoare.

Probability and Random Processes, Second Edition presents pertinent applications to signal processing and communications, two areas of key interest to students and professionals in today's booming communications industry. The book includes unique chapters on narrowband random processes and simulation techniques. It also describes applications in digital communications, information theory, coding theory, image processing, speech analysis, synthesis and recognition, and others. Exceptional exposition and numerous worked out problems make this book extremely readable and accessible. The authors connect the applications discussed in class to the textbook. The new edition contains more real world signal processing and communications applications. It introduces the reader to the basics of probability theory and explores topics ranging from random variables, distributions and density functions to operations on a single random variable. There are also discussions on pairs of random variables; multiple random variables; random sequences and series; random processes in linear systems; Markov processes; and power spectral density. This book is intended for practicing engineers and students in graduate-level courses in the topic. - Exceptional exposition and numerous worked out problems make the book extremely readable and accessible - The authors connect the applications discussed in class to the textbook - The new edition contains more real world signal processing and communications applications - Includes an entire chapter devoted to simulation techniques

Together with the fundamentals of probability, random processes and statistical analysis, this insightful book also presents a broad range of advanced topics and applications. There is extensive coverage of Bayesian vs. frequentist statistics, time series and spectral representation, inequalities, bound and approximation, maximum-likelihood estimation and the expectation-maximization (EM) algorithm, geometric Brownian motion and Itô process. Applications such as hidden Markov models (HMM), the Viterbi, BCJR, and Baum–Welch algorithms, algorithms for machine learning, Wiener and Kalman filters, and queueing and loss networks are treated in detail. The book will be useful to students and researchers in such areas as communications, signal processing, networks, machine learning, bioinformatics, econometrics and mathematical finance. With a solutions manual, lecture slides, supplementary materials and MATLAB programs all available online, it is ideal for classroom teaching as well as a valuable reference for professionals.

This book provides engineers with focused treatment of the mathematics needed to understand probability, random variables, and stochastic processes, which are essential mathematical disciplines used in communications engineering. The author explains the basic concepts of these topics as plainly as possible so that people with no in-depth knowledge of these mathematical topics can better appreciate their applications in real problems. Applications examples are drawn from various areas of communications. If a reader is interested in understanding probability and stochastic processes that are specifically important for communications networks and systems, this book serves his/her need.