References
Math 289A (Spring 2013)
- 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.
- 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.
- 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.)
- 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