Recommended Books for IEOR 6711, Stochastic Models I
Basic Probability Theory (prerequisite)
- A First Course in Probability, sixth edition by Sheldon Ross
Probability Classics
- An Introduction to Probability Theory and its Applications, volume I, third edition by William Feller, 1968.
- An Introduction to Probability Theory and its Applications, volume II, second edition by William Feller, 1971.
Other Stochastic Processes Textbooks (same level)
- Introduction to Stochastic Processes by E. Cinlar, 1975
- Stochastic Models, An Algorithmic Approach by Henk Tijms, 1994
- Adventures in Stochastic Processes by Sid Resnick, Springer, 1992
Measure-Theoretic Probability (a next course)
- A Course in Probability Theory Revised, second edition by Kai Lai Chung, 2000 (paper)
- Probability Essentials, second edition by Jean Jacod and Philip Protter, 2002 (paper)
- Probability by Leo Breiman, Classics in Applied Mathematics 7, SIAM (paper).
- Probability and Measure by Patrick Billingsley, third edition.
- Probability with Martingales by David Williams, (paper)
- Probability and Random Processes by G. R. Grimmett and D. R.
Stirzaker, Oxford University Press (paper)
- A Probability Path by Sid Resnick, Birkhauser
More on Brownian Motion and Diffusion Processes (more advanced, but readable)
- Brownian Motion and Stochastic Flow Systems by J. M. Harrison, 1985, Wiley.
- Brownian Motion and Stochastic Calculus, second edition by Karatzas and Shreve, 2000, Springer.
- A Second Course in Stochastic Processes by Karlin and Taylor, 1981, Academic Press.
Queues
- Introduction to Queueing Theory, second edition by Robert B. Cooper, 1982, North Holland. (engineering focus)
- Applied Probability and Queues, second edition by Soren Asmussen, 2003, Springer. (theoretical focus)
- Queueing Systems, volumes I and II by Leonard Kleinrock, 1975, 1976, Wiley. (engineering focus)
- Queueing Systems: Problems and Solutions by Leonard Kleinrock and Richard Gail, 1996, Wiley. (engineering focus)
- Stochastic Modeling and the Theory of Queues by Ronald Wolff, 1989. (engineering focus)
- Queueing Methods for Services and Manufacturing by Randolph W. Hall, 1991. (introductory, but nice)
Stochastic-Process Limits
- Convergence of Probability Measures, second edition by Patrick Billingsley, 1999, Wiley.
- Markov Processes, Characterization and Convergence by S. N. Ethier and T. G. Kurtz, 1986, Wiley.
- Stochastic-Process Limits by Ward Whitt, 2002, Springer.
Stochastic- Order Relations
- Comparison Methods for Stochastic Models and Risks, second edition
by A. M\"{u}ller and D. Stoyan, 2002, Wiley.
- Stochastic Orders and Their Applications by Moshe Shaked and J. George Shanthikumar, 1994, Academic Press.
Transforms
- Generatingfunctionology, second edition
by Herbert S. Wilf, 2002, Academic Press. (wonderful)
- Integral Transforms and Their Applications, third edition, by Brian Davies, 2002, Springer.
- Operational Calculus by van der Pol and Bremmer, 1955, Chelsea. (classic, hard)
- Transform Techniques for Probability Modeling by Walter C. Giffin, 1975, Academic Press. (introductory)
- Characteristic Functions by Eugene Lukacs, 1970, Hafner. (classic, hard)
- Guide to the Application of Laplace Transforms by Gustav Doetsch, 1961, van Nostrand. (classic, introductory)
- Introduction to the Theory
and Application of the Laplace Transformation by Gustav Doetsch, 1974, Springer. (classic, hard)