Time: | Wednesdays |
Room: | Courant Institute / Warren Weaver Hall 1302 |
Instructor: | Professor Yuri Bakhtin, contact info |
Office hours: | Mondays 1:30 - 3:30 P.M. |
Course description: | The course is targeted at Mathematics PhD students. 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 useful books are: Stochastic Processes by Bass, 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 |
Grading: | 3 or 4 homework assignments will be posted. The homework is to be submitted electronically through NYU Brightspace. No late submissions will be accepted. Homework counts for 60% of the final score. The final exam will count for 40% of the final score. |
Prerequisite: | Fluency with the material of the graduate course Probability Theory I is required. Some but not all of those topics are: measures, Lebesgue integration, various modes of convergence of r.v.'s, characteristic functions, Law of Large Numbers, Central Limit Theorem, conditional expectations w.r.t. sigma-algebras, filtrations, sequences of r.v.'s forming martingales or Markov chains, stopping times, inequalitites for martingales. We will also need elements of functional analysis and real analysis. |
Link to Stochastic Processes by Bass (available through NYU)
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)