An excellent introduction for computer scientists and electrical and electronics engineers who would like to have a good, basic understanding of stochastic processes! This clearly written book responds to the increasing interest in the study of systems that vary in time in a random manner. It presents an introductory account of some of the important topics in the theory of the mathematical models of such systems. The selected topics are conceptually interesting and have fruitful application in various branches of science and technology.
Many probability books are written by mathematicians and have the built in bias that the reader is assumed to be a mathematician coming to the material for its beauty. This textbook is geared towards beginning graduate students from a variety of disciplines whose primary focus is not necessarily mathematics for its own sake. Instead, A Probability Path is designed for those requiring a deep understanding of advanced probability for their research in statistics, applied probability, biology, operations research, mathematical finance, and engineering.
Many probability books are written by mathematicians and have the built-in bias that the reader is assumed to be a mathematician coming to the material for its beauty. This textbook is geared towards beginning graduate students from a variety of disciplines whose primary focus is not necessarily mathematics for its own sake. Instead, A Probability Path is designed for those requiring a deep understanding of advanced probability for their research in statistics, applied probability, biology, operations research, mathematical finance and engineering. A one-semester course is laid out in an efficient and readable manner covering the core material. The first three chapters provide a functioning knowledge of measure theory. Chapter 4 discusses independence, with expectation and integration covered in Chapter 5, followed by topics on different modes of convergence, laws of large numbers with applications to statistics (quantile and distribution function estimation) and applied probability. Two subsequent chapters offer a careful treatment of convergence in distribution and the central limit theorem. The final chapter treats conditional expectation and martingales, closing with a discussion of two fundamental theorems of mathematical finance. Like Adventures in Stochastic Processes, Resnick’s related and very successful textbook, A Probability Path is rich in appropriate examples, illustrations and problems and is suitable for classroom use or self-study. The present uncorrected, softcover reprint is designed to make this classic textbook available to a wider audience. This book is different from the classical textbooks on probability theory in that it treats the measure theoretic background not as a prerequisite but as an integral part of probability theory. The result is that the reader gets a thorough and well-structured framework needed to understand the deeper concepts of current day advanced probability as it is used in statistics, engineering, biology and finance.... The pace of the book is quick and disciplined. Yet there are ample examples sprinkled over the entire book and each chapter finishes with a wealthy section of inspiring problems. —Publications of the International Statistical Institute This textbook offers material for a one-semester course in probability, addressed to students whose primary focus is not necessarily mathematics.... Each chapter is completed by an exercises section. Carefully selected examples enlighten the reader in many situations. The book is an excellent introduction to probability and its applications. —Revue Roumaine de Mathématiques Pures et Appliquées
Brownian Motion and Classical Potential Theory is a six-chapter text that discusses the connection between Brownian motion and classical potential theory. The first three chapters of this book highlight the developing properties of Brownian motion with results from potential theory. The subsequent chapters are devoted to the harmonic and superharmonic functions, as well as the Dirichlet problem. These topics are followed by a discussion on the transient potential theory of Green potentials, with an emphasis on the Newtonian potentials, as well as the recurrent potential theory of logarithmic potentials. The last chapters deal with the application of Brownian motion to obtain the main theorems of classical potential theory. This book will be of value to physicists, chemists, and biologists.
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