Schedule of lectures

Tuesday 2:30-4:00 pm in Jeffery 319

Thursday 1:00-2:30 pm in Jeffery 319

See the daily diary for lecture notes.

Course description

The course will cover selected topics from the book "Brownian Motion. An Introduction to Stochastic Processes" (De Gruyter, 2nd edition) by R.L. Schilling and L. Partzsch.

One of the main themes of the course is the probabilistic solution to partial differential equations such as the heat equation, inhomogeneous initial value problems, and boundary value problems.

We may also study the fine structure of the Brownian motion, including its strong Markov property, its fractal dimensions, its connection to the Laplace operator, Brownian local times, etc.

Another possible topic is the study of Gaussian measures in infinite dimensions, the Lévy Laplacian, and its connection to white noise.

My MATH 895 typed notes are available here. Sections about the Brownian motion (not yet included in the typed notes) are available here (Lévy's construction) and here (properties of the Brownian motion).

Grading scheme

Each participant will deliver several lectures and share their notes with the rest of the class. The grading will take into account the lectures delivered (70%) and in class participation (30%).