Recommended Books for IEOR 6711, Stochastic Models I

Basic Probability Theory (prerequisite)

  1. A First Course in Probability, sixth edition by Sheldon Ross

Probability Classics

  1. An Introduction to Probability Theory and its Applications, volume I, third edition by William Feller, 1968.

  2. An Introduction to Probability Theory and its Applications, volume II, second edition by William Feller, 1971.

Other Stochastic Processes Textbooks (same level)

  1. Introduction to Stochastic Processes by E. Cinlar, 1975

  2. Stochastic Models, An Algorithmic Approach by Henk Tijms, 1994

  3. Adventures in Stochastic Processes by Sid Resnick, Springer, 1992

Measure-Theoretic Probability (a next course)

  1. A Course in Probability Theory Revised, second edition by Kai Lai Chung, 2000 (paper)

  2. Probability Essentials, second edition by Jean Jacod and Philip Protter, 2002 (paper)

  3. Probability by Leo Breiman, Classics in Applied Mathematics 7, SIAM (paper).

  4. Probability and Measure by Patrick Billingsley, third edition.

  5. Probability with Martingales by David Williams, (paper)

  6. Probability and Random Processes by G. R. Grimmett and D. R. Stirzaker, Oxford University Press (paper)

  7. A Probability Path by Sid Resnick, Birkhauser

More on Brownian Motion and Diffusion Processes (more advanced, but readable)

  1. Brownian Motion and Stochastic Flow Systems by J. M. Harrison, 1985, Wiley.

  2. Brownian Motion and Stochastic Calculus, second edition by Karatzas and Shreve, 2000, Springer.

  3. A Second Course in Stochastic Processes by Karlin and Taylor, 1981, Academic Press.

Queues

  1. Introduction to Queueing Theory, second edition by Robert B. Cooper, 1982, North Holland. (engineering focus)

  2. Applied Probability and Queues, second edition by Soren Asmussen, 2003, Springer. (theoretical focus)

  3. Queueing Systems, volumes I and II by Leonard Kleinrock, 1975, 1976, Wiley. (engineering focus)

  4. Queueing Systems: Problems and Solutions by Leonard Kleinrock and Richard Gail, 1996, Wiley. (engineering focus)

  5. Stochastic Modeling and the Theory of Queues by Ronald Wolff, 1989. (engineering focus)

  6. Queueing Methods for Services and Manufacturing by Randolph W. Hall, 1991. (introductory, but nice)

Stochastic-Process Limits

  1. Convergence of Probability Measures, second edition by Patrick Billingsley, 1999, Wiley.

  2. Markov Processes, Characterization and Convergence by S. N. Ethier and T. G. Kurtz, 1986, Wiley.

  3. Stochastic-Process Limits by Ward Whitt, 2002, Springer.

Stochastic- Order Relations

  1. Comparison Methods for Stochastic Models and Risks, second edition by A. M\"{u}ller and D. Stoyan, 2002, Wiley.

  2. Stochastic Orders and Their Applications by Moshe Shaked and J. George Shanthikumar, 1994, Academic Press.

Transforms

  1. Generatingfunctionology, second edition by Herbert S. Wilf, 2002, Academic Press. (wonderful)

  2. Integral Transforms and Their Applications, third edition, by Brian Davies, 2002, Springer.

  3. Operational Calculus by van der Pol and Bremmer, 1955, Chelsea. (classic, hard)

  4. Transform Techniques for Probability Modeling by Walter C. Giffin, 1975, Academic Press. (introductory)

  5. Characteristic Functions by Eugene Lukacs, 1970, Hafner. (classic, hard)

  6. Guide to the Application of Laplace Transforms by Gustav Doetsch, 1961, van Nostrand. (classic, introductory)

  7. Introduction to the Theory and Application of the Laplace Transformation by Gustav Doetsch, 1974, Springer. (classic, hard)