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.
Table of Contents:
PROBABILITY THEORY
RANDOM EVENTS AND THEIR PROBABILITIES
RANDOM EXPERIMENTS
RANDOM EVENTS
PROBABILITY
CONDITIONAL PROBABILITY AND INDEPENDENCE OF RANDOM EVENTS
ONE-DIMENSIONAL RANDOM VARIABLES
MOTIVATION AND TERMINOLOGY
DISCRETE RANDOM VARIABLES
CONTINUOUS RANDOM VARIABLES
MIXTURES OF RANDOM VARIABLES
GENERATING FUNCTIONS
MULTIDIMENSIONAL RANDOM VARIABLES
TWO-DIMENSIONAL RANDOM VARIABLES
n-DIMENSIONAL RANDOM VARIABLES
FUNCTIONS OF RANDOM VARIABLES
FUNCTIONS OF ONE RANDOM VARIABLE
FUNCTIONS OF SEVERAL RANDOM VARIABLES
SUMS OF RANDOM VARIABLES
INEQUALITIES AND LIMIT THEOREMS
INEQUALITIES
LIMIT THEOREMS
STOCHASTIC PROCESSES
BASICS OF STOCHASTIC PROCESSES
MOTIVATION AND TERMINOLOGY
CHARACTERISTICS AND EXAMPLES
CLASSIFICATION OF STOCHASTIC PROCESSES
TIME SERIES IN DISCRETE TIME
RANDOM POINT PROCESSES
BASIC CONCEPTS
POISSON PROCESSES
RENEWAL PROCESSES
DISCRETE-TIME MARKOV CHAINS
FOUNDATIONS AND EXAMPLES
CLASSIFICATION OF STATES
LIMIT THEOREMS AND STATIONARY DISTRIBUTION
BIRTH AND DEATH PROCESSES
DISCRETE-TIME BRANCHING PROCESSES
CONTINUOUS-TIME MARKOV CHAINS
BASIC 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
MARTINGALES
DISCRETE-TIME MARTINGALES
CONTINUOUS-TIME MARTINGALES
BROWNIAN MOTION
INTRODUCTION
PROPERTIES OF THE BROWNIAN MOTION
MULTIDIMENSIONAL AND CONDITIONAL DISTRIBUTIONS
FIRST PASSAGE TIMES
TRANSFORMATIONS OF THE BROWNIAN MOTION
SPECTRAL ANALYSIS OF STATIONARY PROCESSES
FOUNDATIONS
PROCESSES WITH DISCRETE SPECTRUM
PROCESSES WITH CONTINUOUS SPECTRUM
REFERENCES
INDEX
Exercises appear at the end of each chapter.
