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# Recommended Resources in Probability Theory and Stochastic Processes Randall J. Swift

DOI link for Recommended Resources in Probability Theory and Stochastic Processes Randall J. Swift

Recommended Resources in Probability Theory and Stochastic Processes Randall J. Swift book

# Recommended Resources in Probability Theory and Stochastic Processes Randall J. Swift

DOI link for Recommended Resources in Probability Theory and Stochastic Processes Randall J. Swift

Recommended Resources in Probability Theory and Stochastic Processes Randall J. Swift book

## ABSTRACT

I. General Probability Theory and Stochastic Processes 254A. Introductory sources 254B. Advanced introductory texts with broad coverage 256C. Major journals and serial publications 257D. Other printed resources 260E. Online resources 260II. Foundations of Probability Theory 261III. Probability on Algebraic and Topological Structures 262IV. Combinatorial Probability 263V. Limit Theorems 263VI. Stochastic Processes 265A. Useful support texts 265B. Filtering theory 265C. General theory of random fields 266D. Gaussian processes 266E. Martingale theory 266F. Second-order processes and fields 267VII. Stochastic Analysis 267A. Texts with general coverage 267B. Stochastic integration 268 253

c. Stochastic differential equations 269D. Malliavin calculus 269Queueing Theory 270 A. Journals devoted to queueing theory 270B. Introductory texts 270Special Processes 271 A. Brownian motion 271B. Levy processes 271 C. Point processes 271D. Poisson processes 272 E. Birth-death processes 272

It is generally felt that there are two approaches to the study of probability theory. One approach is a heuristic, nonrigorous, set theoretic treatment that develops the student’s intuitive feel for the subject. This approach is calculus-based and enables students to “think probabilistically.” The other approach is based upon measure theory, which is the mathematical foundation of the subject. A thorough understanding of measure theory is necessary for a deep, proper study of probability theory.Probability texts at the undergraduate level are based upon the intuitive approach and there are some excellent texts that develop the ability to apply probability to problems in such fields as engineering, management science, and the physical and social sciences. Most of these texts include a treatment of statistics. A few of my favorites, listed alphabetically, are the following. R Hogg and A Craig. Introduction to Mathematical Statistics. 4th ed. New York: Macmillan, 1978.This is a classic text on mathematical statistics that treats the probability distributions with an eye towards their use in mathematical statistics. R Hogg and E Tanis. Probability and Statistical Inference. 5th ed. New York: Macmillan, 1997.This is an excellent text that begins with elementary probability theory, develops the standard probability distributions, and gives a very thorough treatment of statistical inference.