Prerequisite: Probability II.

Processes in continuous time: independent increments, martingales. Markov processes: construction, Hille-Yosida theorem, basic properties, Feller processes. Stochastic integration and diffusions. Other topics according to the interests of the instructor and the class.

References:
BILLINGSLEY, P. – Convergence of Probability Measures. New York, J. Wiley, 1968.
KARATZAS, I., SHREVE, S. – Brownian Motion and Stochastic Calculus (2nd edition). New York, Springer-Verlag, 2008.
REVUZ, D., YOR, M. – Continuous Martingales and Brownian Motion (3rd edition). New York, Springer-Verlag, 2004.
ROGERS, L. C. G., WILLIAMS, D. – Diffusions, Markov Processes, and Martingales, Vol 1: Foundations, Cambridge, Cambridge University Press, 2000.
ROGERS, L. C. G., WILLIAMS, D. – Diffusions, Markov Processes, and Martingales, Vol 2: Itô Calculus, Cambridge, Cambridge University Press, 2000.
VARADHAN, S.R.S. – Stochastic Processes, New York, Courant Institute of Mathemetical Sciences, 2001.

* Basic syllabus. The teacher has the autonomy to make any changes.