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Lectures: Monday, Wednesday and Friday, 1pm-2pm, in Science Center 216.

Lecturer: Paul Bourgade, office hours Tuesday and Thursday 10:30am-12pm, you also can email me (bourgade@math.harvard.edu) to set up an appointment or just drop by (Science Center 341).

Lecture notes available here, soon complete. Please let me know about the inaccuracies and typos you will certainly find.

Course description: introduction to continuous stochastic processes, and connections with other mathematical fields (harmonic analysis, concentration of measure, trace formulae).

Prerequisites: you need to be familiar with basic probability theory (random variables, conditional expectation, convergence types). For the last month of lectures, some acquaintance with differential geometry will be useful, but not necessary, the required notions being briefly introduced.

Textbooks: Recommended texts are: Probability Essentials by Jacod-Protter for prerequisites, Multidimensional Diffusion Processes by Stroock-Varadhan and Continuous martingales and Brownian motion by Revuz-Yor.

Grading: problem sets (50%) and a final project (50%).

The course covers the following topics:

Problem sets. The students talks, Science Center, 341.