Introduction to probability and stochastic processes with applications

This text book is designed for a one-year course in probability and stochastic processes with applications, especially for students who wish to specialize in probabilistic modeling. This book bridges the gap between elementary texts and advanced texts in probability and is easily accessible for students with diverse backgrounds and majoring in engineering, applied sciences, business and finance, statistics, mathematics, and operations research. The text contains many examples and exercises which have been tested in classrooms and are chosen from diverse areas such as queuing models, reliability and finance. Chapter coverage includes: basic concepts, random variables and their distributions, discrete distributions, continuous distributions, random vectors, multivariate normal distributions, conditional expectation, limit theorems, stochastic processes, queuing models, stochastic calculus, and mathematical finance.

Basic Concepts. Random Variables and their Distributions. Some Discrete Distributions. Some Continuous Distributions. Random Vectors. Conditional Expectation. Multivariate Normal Distribution. Limit Theorems. Introduction to Stochastic Processes. Introduction to Queueing Models. Stochastic Calculus. Introduction to Mathematical Finance. Exercises. Appendix A. Basic Concepts on Set Theory. Appendix B. Introduction to Combinatorics. Appendix C. Topics on Linear Algebra. Appendix D. Statistical Tables. Problem Solutions. References. Bibliography. Glossary. Index.

LILIANA BLANCO CASTAÑEDA, DrRerNat, is Associate Professor in the Department of Statistics at the National University of Colombia and the author of several journal articles and three books on basic and advanced probability.

VISWANATHAN ARUNACHALAM, PhD, is Associate Professor in the Department of Mathematics at the Universidad de los Andes, Colombia. He has published numerous journal articles in areas such as optimization, stochastic processes, and the mathematics of financial derivatives.

SELVAMUTHU DHARMARAJA, PhD, is Associate Professor in the Department of Mathematics and the Bharti School of Telecommunication Technology and Management at the Indian Institute of Technology Delhi. The author of several journal articles, he is Associate Editor for the International Journal of Communication Systems.