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Full Description
Applied Probability and Stochastic Processes, Second Edition presents a self-contained introduction to elementary probability theory and stochastic processes with a special emphasis on their applications in science, engineering, finance, computer science, and operations research. It covers the theoretical foundations for modeling time-dependent random phenomena in these areas and illustrates applications through the analysis of numerous practical examples. The author draws on his 50 years of experience in the field to give your students a better understanding of probability theory and stochastic processes and enable them to use stochastic modeling in their work.
New to the Second Edition
Completely rewritten part on probability theory—now more than double in size
New sections on time series analysis, random walks, branching processes, and spectral analysis of stationary stochastic processes
Comprehensive numerical discussions of examples, which replace the more theoretically challenging sections
Additional examples, exercises, and figures
Presenting the material in a student-friendly, application-oriented manner, this non-measure theoretic text only assumes a mathematical maturity that applied science students acquire during their undergraduate studies in mathematics. Many exercises allow students to assess their understanding of the topics. In addition, the book occasionally describes connections between probabilistic concepts and corresponding statistical approaches to facilitate comprehension. Some important proofs and challenging examples and exercises are also included for more theoretically interested readers.
Contents
PROBABILITY THEORY: RANDOM EVENTS AND THEIR PROBABILITIES. ONE-DIMENSIONAL RANDOM VARIABLES. MULTIDIMENSIONAL RANDOM VARIABLES. FUNCTIONS OF RANDOM VARIABLES. INEQUALITIES AND LIMIT THEOREMS. STOCHASTIC PROCESSES: BASICS OF STOCHASTIC PROCESSES. RANDOM POINT PROCESSES. DISCRETE-TIME MARKOV CHAINS. CONTINUOUS-TIME MARKOV CHAINS. MARTINGALES. BROWNIAN MOTION. SPECTRAL ANALYSIS OF STATIONARY PROCESSES. REFERENCES. INDEX.
