Graduate student reading seminar
Tuesdays at 2:30pm, VV B305 for the rest of the semester
2014 Fall
9/23: Dave
I will go over Mike Giles’ 2008 paper “Multi-level Monte Carlo path simulation.” This paper introduced a new Monte Carlo method to approximate expectations of SDEs (driven by Brownian motions) that is significantly more efficient than what was the state of the art. This work opened up a whole new field in the numerical analysis of stochastic processes as the basic idea is quite flexible and has found a variety of applications including SDEs driven by Brownian motions, Levy-driven SDEs, SPDEs, and models from biology
9/30: Benedek
A very quick introduction to Stein's method.
I will give a brief introduction to Stein's method, mostly based on the the first couple of sections of the following survey article:
Ross, N. (2011). Fundamentals of Stein’s method. Probability Surveys, 8, 210-293.
The following webpage has a huge collection of resources if you want to go deeper: Stein's method https://sites.google.com/site/yvikswan/about-stein-s-method
Note that the Midwest Probability Colloquium (http://www.math.northwestern.edu/mwp/) will have a tutorial program on Stein's method this year.
10/7, 10/14: Chris
10/21, 10/28: Dae Han
11/4, 11/11: Elnur
11/18, 11/25: Chris
12/2, 12/9: Yun Zhai
2014 Spring
1/28: Greg
2/04, 2/11: Scott
Reflected Brownian motion, Occupation time, and applications.
2/18: Phil-- Examples of structure results in probability theory.
2/25, 3/4: Beth-- Derivative estimation for discrete time Markov chains
3/11, 3/25: Chris J Some classical results on stationary distributions of Markov processes
4/1, 4/8: Chris N
4/15, 4/22: Yu Sun
4/29. 5/6: Diane
2013 Fall
9/24, 10/1: Chris A light introduction to metastability
10/8, Dae Han Majoring multiplicative cascades for directed polymers in random media
10/15, 10/22: no reading seminar
10/29, 11/5: Elnur Limit fluctuations of last passage times
11/12: Yun Helffer-Sj?ostrand representation and Brascamp-Lieb inequality for stochastic interface models
11/19, 11/26: Yu Sun
12/3, 12/10: Jason
2013 Spring
2/13: Elnur
Young diagrams, RSK correspondence, corner growth models, distribution of last passage times.
2/20: Elnur
2/27: Chris
A brief introduction to enlargement of filtration and the Dufresne identity Notes
3/6: Chris
3/13: Dae Han
An introduction to random polymers
3/20: Dae Han
Directed polymers in a random environment: path localization and strong disorder
4/3: Diane
Scale and Speed for honest 1 dimensional diffusions
References:
Rogers & Williams - Diffusions, Markov Processes and Martingales
Ito & McKean - Diffusion Processes and their Sample Paths
Breiman - Probability
http://www.statslab.cam.ac.uk/~beresty/Articles/diffusions.pdf
4/10: Diane
4/17: Yun
Introduction to stochastic interface models
4/24: Yun
Dynamics and Gaussian equilibrium sytems
5/1: This reading seminar will be shifted because of a probability seminar.
5/8: Greg, Maso
The Bethe ansatz vs. The Replica Trick. This lecture is an overview of the two approaches. See [1] for a nice overview.
5/15: Greg, Maso
Rigorous use of the replica trick.