APMA 2812B - Fall 2019

Below is a course schedule. It contains an outline of course topics, reading assignments, and important due dates. Most readings will be assigned from the course notes.

Note: This schedule is approximate and will evolve as the course progresses. Lectures may be rearranged and split between days.

Date	Material	Info/Reading
	Introduction
Week 1: Fri 9/6	Introduction, motivating examples, preliminaries	§ 1, 2
	Gaussian measure theory
Week 2: Fri 9/13	Gaussian measures in separable Banach spaces, Fernique theorem, Cameron-Martin theorem	§ 3.1 , 3.2, 3.3
Week 3: Fri 9/20	Probability measures in Hilbert spaces, Trace-class operators, Feldman-Hajek theorem, Gaussian processes and regularity	§ 3.4 , 3.5
	The stochastic integral
Week 4: Fri 9/27	Wiener processes in Hilbert spaces, cylindrical Wiener process, progressive measurability	§ 3.6 - 4.4
Week 5: Fri 10/4	The stochastic integral and properties	Homework 1 Due § 4.5 , 4.6
Week 6: Fri 10/11	Ito's formula and stochastic Fubini	§ 4.7, 4.8
	Introduction to semi-group theory
Week 7: Fri 10/18	$C_0$ semi-groups, generators, Hille-Yosida theorem, spectral theory	§ 5.1 - 5.3
Week 8: Fri 10/25	Analytic semi-groups, regularity and interpolation spaces	§ 5.4 - 5.6
	Linear SPDE with additive noise	§ 6.1 -
Week 9: Fri 11/1	Mild solutions, stochastic convolution, regularity
	Semi-linear SPDE with additive noise
Week 10: Fri 11/8	Cancelled
Week 11: Fri 11/15	Lipschitz non-linearities, global well-posedness, locally Lipschitz non-linearities, non-explosion criteria
	Long-time behavior
Week 12: Fri 11/22	Markov semi-groups, Krylov-Bogoliubov theorem, uniqueness and strong Feller for Linear SPDE
Fri 10/29	Thanksgiving break (Black Friday) - No Class
Week 13: Fri 12/6	Geometric ergodicity, Lyapunov functions, Harris theorem, application to linear SPDE	Homework 3 Due

Course Schedule APMA 2812B - Fall 2019

Course Schedule
APMA 2812B - Fall 2019