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- Text: Continuous Time Markov Processes (Graduate Studies in Mathematics), by Thomas M. Liggett. Publisher: American Mathematical Society, 2010.

- References:

- Markov Processes, Characterization and Convergence. By Stewart N. Ethier and Thomas G. Kurtz. Publisher: Wiley. 1986.
- Stochastic Processes. By Richard F. Bass. Publisher: Cambridge University Press. 2011.
- Brownian Motion and Stochastic Calculus. (Graduate Text in Mathematics) By Ioannis Karatzas and Steven E. Shreve. Publisher: Springer. 1998.

- Prerequisite: Math 865 or permission of the instructor.

- Office: 510 Snow Hall; Office hour (through zoom video conference): Since the teaching has moved to online, office hour will be made on an individual basis by appointment. The normal times are Tuesday, Thursday 2:00-3:00 pm, but other times may be good too.

- Lecture time: Tuesday and Thursday. 11:00am-12:15 pm through zoom video conference.

- Exams: Midterm exams will be given in the form of exercises. Final exams will be given in the form of mini-research/reading/presentation project.

- Course coverage: Brownian Motion, Markov Chains, Stochastic Integrations, Feller Process, Interacting particle systems, Martingale theory and Martingale Problems, linear parabolic and elliptic PDEs, Applications, etc…