Probability and Stochastic Modeling

Vladimir I. Rotar is a professor in the Department of Mathematics and Statistics at San Diego State University. Dr. Rotar has authored four books and more than 100 scientific papers on probability theory and its applications in leading mathematical journals.

Basic Notions. Independence and Conditional Probability. Discrete Random Variables. Generating Functions. Branching Processes. Random Walk Revisited. Markov Chains. Continuous Random Variables. Distributions in the General Case. Simulation. Moment Generating Functions. The Central Limit Theorem for Independent Random Variables. Covariance Analysis. The Multivariate Normal Distribution. The Multivariate Central Limit Theorem. Maxima and Minima of Random Variables. Elements of Reliability Theory. Hazard Rate and Survival Probabilities. Stochastic Processes: Preliminaries. Counting and Queuing Processes. Birth and Death Processes: A General Scheme. Elements of Renewal Theory. Martingales in Discrete Time. Brownian Motion and Martingales in Continuous Time. More on Dependency Structures. Comparison of Random Variables. Risk Evaluation. Appendix. References. Answers to Exercises. Index.