MS&E 321

Stochastic Systems


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References


General Probability:

  • Ross, S.M. (1980). Introduction to Probability Models, Second Edition. Academic Press, New York. (Chapters 1, 2 and 3)
  • Breiman, L. (1968). Probability. Addison-Wesley, Reading, Massachusetts.
  • Billingsley, P. (1979). Probability and Measure. John Wiley, New York.
  • Feller, W. (1957). An Introduction to Probability Theory and Its Applications, Vol. 1. John Wiley & Sons, New York.
  • Feller, W. (1971). An Introduction to Probability Theory and Its Applications, Vol. 2. John Wiley & Sons, New York.
  • Renyi, A. (1970). Foundations of Probability. Holden-Day, San Francisco, California.
  • Chung, K.L. (1968). A Course in Probability. Harcourt, Brace and World, New York.
  • Gnedenko, B.V. and A.N. Kolmogorov (1954). Limit Distributions for Sums of Independent Random Variables. Addison-Wesley, Reading, Massachusetts (Translation from Russian).

General Stochastic Processes:

  • Cinlar, E. (1975). Introduction to Stochastic Processes. Prentice-Hall, Englewood Cliffs, New Jersey.
  • Cox, D.R. and H.D. Miller (1965). The Theory of Stochastic Processes. John Wiley & Sons, New York.
  • Doob, J.L. (1953). Stochastic Processes.  John Wiley & Sons, New York.
  • Taylor, H.M. and S. Karlin (1984). An Introduction to Stochastic Modeling. Academic Press, New York.
  • Parzen, E. (1962). Stochastic Processes. Holden-Day, San Francisco, California.
  • Prabhu, N.U. (1965). Stochastic Processes. Macmillan, New York.
  • Spitzer, F. (1964). Random Walks. Von Nostrand. Princeton, New Jersey.

Discrete-time Markov Chains (DTMCs):

Continuous-time Markov Chains (DTMCs):

Stability for General State Space Markov Chains:

  • S.P. Meyn and R.L. Tweedie (1993). Markov Chains and Stochastic Stability. Springer-Verlag, New York.

Stochastic Control

Diffusion Approximations and Brownian motion:

Renewal Theory:

Queueing Theory:

  • Asmussen, S. (2003). Applied Probability and Queues. 2nd ed, Springer.
  • Gross, D. and C. Harris (1985). Fundamentals of Queueing Theory, Second Edition. Wiley, New York.
  • Cox, D.R. and W.L. Smith (1961). Queues.? Methuen, London.
  • Gross, D. and C. Harris (1985). Fundamentals of Queueing Theory, Second Edition. Wiley, New York.
  • Tijms, H. (1986). Stochastic Modeling and Analysis-A Computational Approach. John Wiley & Sons, New York.

Algorithms

  • Tijms, H. (1986). Stochastic Modeling and Analysis-A Computational Approach. John Wiley & Sons, New York.
  • Bremaud, P. Markov Chains: Gibbs Fields, Monte Carlo Simulation, and Queues. Springer.



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