Math 289A (Spring 2013)

  1. Markov Chains
    • Norris, J. R.: Markov chains, Cambridge University Press, Cambridge, 1998.
    • Chung, K.L.: Markov chains with stationary transition probabilities, Springer-Verlag, Berlin-Goettingen-Heidelberg, 1960.
  2. Markovian Loops
    • Le Jan, Y.: Markov loops and renormalization, Annals of Probability, vol. 38 (2010) pp. 1280-1319. [Click here for a downloadable version of this paper.]
    • Le Jan, Y.: Markov paths, loops and fields, Lecture Notes in Mathematics 2026. Springer, Heidelberg, 2011. [Click here for a downloadable version of this paper.]
    • Sznitman, A.-S.: Topics in occupation times and Gaussian free fields, European Mathematical Society, Zurich, 2012.
  3. Poisson Processes
    • Kingman, J.F.C.: Poisson Processes, Oxford University Press, New York, 1993.
    • Cinlar, E.: Probability and Stochastics, Springer, New York, 2011. (Especially Chapter VI. Available online from UCSD addresses here.)
  4. Brownian Motion and its Local Time
    • Chung, K. L., Williams, R. J.: Introduction to stochastic integration (Second edition).
      Birkhauser, Boston, MA, 1990.
    • Morters, Peter, Peres, Yuval: Brownian motion.
      Cambridge University Press, Cambridge, 2010. (A pdf of this book can be downloaded here.)
    • Revuz, Daniel, Yor, Marc: Continuous martingales and Brownian motion (Third edition).
      Springer-Verlag, Berlin, 1999. (Available online from UCSD addresses here.)
    • Rogers, L. C. G., Williams, David: Diffusions, Markov processes, and martingales. Vol. 1. Foundations.
      Cambridge University Press, Cambridge, 2000.

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Last updated April 24, 2013