Applied Probability and Stochastic Processes, Second Edition

Beichelt offers numerous worked examples to represent stochastic processes in a user-friendly way. He includes a review of probability-theoretic topics and provides important proofs and theoretically challenging examples for the mathematically interested reader. 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 PROBABILITY THEORYRANDOM EVENTS AND THEIR PROBABILITIESRANDOM EXPERIMENTS RANDOM EVENTS PROBABILITY CONDITIONAL PROBABILITY AND INDEPENDENCE OF RANDOM EVENTS ONE-DIMENSIONAL RANDOM VARIABLESMOTIVATION AND TERMINOLOGY DISCRETE RANDOM VARIABLES CONTINUOUS RANDOM VARIABLES MIXTURES OF RANDOM VARIABLES GENERATING FUNCTIONS MULTIDIMENSIONAL RANDOM VARIABLESTWO-DIMENSIONAL RANDOM VARIABLES n-DIMENSIONAL RANDOM VARIABLES FUNCTIONS OF RANDOM VARIABLESFUNCTIONS OF ONE RANDOM VARIABLE FUNCTIONS OF SEVERAL RANDOM VARIABLES SUMS OF RANDOM VARIABLES INEQUALITIES AND LIMIT THEOREMSINEQUALITIES LIMIT THEOREMS STOCHASTIC PROCESSESBASICS OF STOCHASTIC PROCESSESMOTIVATION AND TERMINOLOGY CHARACTERISTICS AND EXAMPLES CLASSIFICATION OF STOCHASTIC PROCESSES TIME SERIES IN DISCRETE TIME RANDOM POINT PROCESSESBASIC CONCEPTS POISSON PROCESSES RENEWAL PROCESSES DISCRETE-TIME MARKOV CHAINSFOUNDATIONS AND EXAMPLES CLASSIFICATION OF STATES LIMIT THEOREMS AND STATIONARY DISTRIBUTION BIRTH AND DEATH PROCESSES DISCRETE-TIME BRANCHING PROCESSES CONTINUOUS-TIME MARKOV CHAINSBASIC CONCEPTS AND EXAMPLES TRANSITION PROBABILITIES AND RATES STATIONARY STATE PROBABILITIES SOJOURN TIMES IN PROCESS STATES CONSTRUCTION OF MARKOV SYSTEMS BIRTH AND DEATH PROCESSES APPLICATIONS TO QUEUEING MODELS SEMI-MARKOV CHAINS MARTINGALESDISCRETE-TIME MARTINGALES CONTINUOUS-TIME MARTINGALES BROWNIAN MOTIONINTRODUCTION PROPERTIES OF THE BROWNIAN MOTION MULTIDIMENSIONAL AND CONDITIONAL DISTRIBUTIONS FIRST PASSAGE TIMESTRANSFORMATIONS OF THE BROWNIAN MOTION SPECTRAL ANALYSIS OF STATIONARY PROCESSESFOUNDATIONS PROCESSES WITH DISCRETE SPECTRUM PROCESSES WITH CONTINUOUS SPECTRUM REFERENCES INDEX Exercises appear at the end of each chapter.