Basics Of Applied Stochastic Processes

Basics of Applied Stochastic Processes

Stochastic processes are mathematical models of random phenomena that evolve according to prescribed dynamics. Processes commonly used in applications are Markov chains in discrete and continuous time, renewal and regenerative processes, Poisson processes, and Brownian motion. This volume gives an in-depth description of the structure and basic properties of these stochastic processes. A main focus is on equilibrium distributions, strong laws of large numbers, and ordinary and functional central limit theorems for cost and performance parameters. Although these results differ for various processes, they have a common trait of being limit theorems for processes with regenerative increments. Extensive examples and exercises show how to formulate stochastic models of systems as functions of a system’s data and dynamics, and how to represent and analyze cost and performance measures. Topics include stochastic networks, spatial and space-time Poisson processes, queueing, reversible processes, simulation, Brownian approximations, and varied Markovian models. The technical level of the volume is between that of introductory texts that focus on highlights of applied stochastic processes, and advanced texts that focus on theoretical aspects of processes.

Applied Stochastic Processes

Applied Stochastic Processes uses a distinctly applied framework to present the most important topics in the field of stochastic processes. Key features: -Presents carefully chosen topics such as Gaussian and Markovian processes, Markov chains, Poisson processes, Brownian motion, and queueing theory -Examines in detail special diffusion processes, with implications for finance, various generalizations of Poisson processes, and renewal processes -Serves graduate students in a variety of disciplines such as applied mathematics, operations research, engineering, finance, and business administration -Contains numerous examples and approximately 350 advanced problems, reinforcing both concepts and applications -Includes entertaining mini-biographies of mathematicians, giving an enriching historical context -Covers basic results in probability Two appendices with statistical tables and solutions to the even-numbered problems are included at the end. This textbook is for graduate students in applied mathematics, operations research, and engineering. Pure mathematics students interested in the applications of probability and stochastic processes and students in business administration will also find this book useful.

A Course in Applied Stochastic Processes