Course: | MATH-GA 2912.001 Probability: Limit Theorems II, Spring 2018 |
Time: | Wednesdays |
Room: | Courant Institute / Warren Weaver Hall 202 |
Instructor: | Professor Yuri Bakhtin, contact info |
Office hours: | Mondays 1:30-3:30 P.M. |
Course description: | Stochastic processes in continuous time. Brownian motion. Poisson process. Processes with independent increments. Stationary processes. Semi-martingales. Markov processes and the associated semi-groups. Connections with PDEs. Stochastic differential equations. Convergence of processes. |
Text: | There will be no official textbook. Some very useful books are: Stochastic Processes by Varadhan (Courant Lecture Series in Mathematics, volume 16), Theory of Probability and Random Processes by Koralov and Sinai, Brownian Motion and Stochastic Calculus by Karatzas and Shreve, Continuous Martingales and Brownian Motion by Revuz and Yor, Markov Processes: Characterization and Convergence by Ethier and Kurtz, Convergence of Probability Measures by Billingsley, Stochastic Processes by Bass. |
Problem sets: | Will be available on this page, to be submitted for grading approximately every 2-3 weeks, must be submitted before the end of class on the due date. 40% of the final grade is based on the homework. |
Final: | There will be a take-home final exam worth 60% of the final grade |
Prerequisite: | Probability: Limit Theorems I |
Link to Brownian Motion and Stochastic Calculus by Karatzas and Shreve (available through NYU)
Link to Theory of Probability and Random Processes by Koralov and Sinai (available through NYU)
Link to Continuous Martingales and Brownian Motion by Revuz and Yor (available through NYU)