Probability and Random Processes

This textbook introduces readers to the fundamental notions of modern probability theory. The only prerequisite is a working knowledge in real analysis. Highlighting the connections between martingales and Markov chains on one hand, and Brownian motion and harmonic functions on the other, this book provides an introduction to the rich interplay between probability and other areas of analysis.Arranged into three parts, the book begins with a rigorous treatment of measure theory, with applications to probability in mind. The second part of the book focuses on the basic concepts of probability theory such as random variables, independence, conditional expectation, and the different types of convergence of random variables. In the third part, in which all chapters can be read independently, the reader will encounter three important classes of stochastic processes: discrete-time martingales, countable state-space Markov chains, and Brownian motion. Each chapter ends with a selection of illu

Eleven types of armors were laboratory tested and their performances concerning the random placements of armors for two different surface slopes of rubble mound breakwater were compared. The three major categories of performance comparison are wave reflection, wave run-up and run-down, and armor stability. Due to the vast differences both in the setups of experiments and in the methodologies of data acquisition and analyses, the multitude of existing literatures yielded extremely scattering results, which are generally quite inconclusive and inconsistent, as well as incomparable. To cope with these problems the present research carries out the following: (1) Factors that affect armor behaviors are detailed and those that are modeled or not are indicated; (2) A real time laboratory system for data acquisition, monitoring, calibration, and analyses is developed, and the integrated program aims to provide accurate, convenient, and automated on-site processes; (3) Based upon the intrinsic

Heavy tails –extreme events or values more common than expected –emerge everywhere: the economy, natural events, and social and information networks are just a few examples. Yet after decades of progress, they are still treated as mysterious, surprising, and even controversial, primarily because the necessary mathematical models and statistical methods are not widely known. This book, for the first time, provides a rigorous introduction to heavy-tailed distributions accessible to anyone who knows elementary probability. It tackles and tames the zoo of terminology for models and properties, demystifying topics such as the generalized central limit theorem and regular variation. It tracks the natural emergence of heavy-tailed distributions from a wide variety of general processes, building intuition. And it reveals the controversy surrounding heavy tails to be the result of flawed statistics, then equips readers to identify and estimate with confidence. Over 100 exercises complete this e

Introduction to Reliability Engineering A complete revision of the classic text on reliability engineering, written by an expanded author team with increased industry perspective Introduction to Reliability Engineering provides a thorough and well-balanced overview of the fundamental aspects of reliability engineering and describes the role of probability and statistical analysis in predicting and evaluating reliability in a range of engineering applications. Covering both foundational theory and real-world practice, this classic textbook helps students of any engineering discipline understand key probability concepts, random variables and their use in reliability, Weibull analysis, system safety analysis, reliability and environmental stress testing, redundancy, failure interactions, and more. Extensively revised to meet the needs of today’s students, the Third Edition fully reflects current industrial practices and provides a wealth of new examples and problems that no

《數理統計(第2版)(英文版)》內容簡介：Probability Theory、Probability Spaces and Random Elements、σ－fields and measures、Measurable functions and distributions、Integration and Differentiation、Integration、Radon.Nikodym de