Teaching

MA 515/STAT 540: Mathematics of Finance. Syllabus
MA 516/STAT 541: Advanced Probability and Options, with Numerical Methods. Syllabus
MA/STAT 532: Applied Stochastic Processes. Syllabus
MA/STAT 598 T: Stochastic Partial Differential Equations. Syllabus
MA/STAT 598 U: Stochastic Partial Differential Equations II: with Fractional Brownian Motion.
MA/STAT 519: Introduction to Probability Theory Syllabus
MA/STAT 638: Stochastic Processes. Syllabus
MA/STAT 639: Stochastic Processes II: with Gaussian Stochastic Analysis. Syllabus
MA598U/STAT598W: Design and Analyis of Financial Algorithms. Syllabus
STAT 311: Introductory Probability. Syllabus
STAT 472: Actuarial Models I. Syllabus
STAT 473: Actuarial Models II. Syllabus

Reading lists (archive)

Reading list for MA/STAT 598T (pdf format):

Group 1: Lyapunov upper bound on non-flat space Tindel-Viens [32]
Group 2: Exact Lyapunov Exponent for discrete space-time white noise potential Cranston-Mountford-Shiga [10]
Group 3: Stochastic Filtering / Branching and Interacting Particle Systems Crisan-Gaines-Lyons [11] and/or Tindel-Viens [34]
Group 4: Lyapunov lower bound for Holder-continuous potential Tindel-Viens [33]
Group 5: Gaussian regularity theory Tindel-Viens Chap 5 (Holder regularity for SPDE on Lie Groups) [30] and/or Tindel-Tudor-Viens Section 5.1 (Sharp Gaussian Regularity) [29] and/or R. Adler. An introduction to continuity, Extrema, and related topics for general Gaussian processes IMS Lect. Notes, 12, 1990. Chapter 4.; and/or M. Talagrand. Regularity of Gaussian Processes. Acta Math. 159 (1987) no. 1-2, 99-149.
Group 6: Fractional Brownian motion. Tindel-Tudor-Viens Chapter 6 (a fractional stochastic Feynman-Kac formula) [29]

Reading list for MA/STAT 598U (pdf format):

Stochastic calculus for fBm with H>1/2 (E. Alos and D. Nualart) Alos-Nualart
Stochastic calculus for fBm with H<1/2 (E. Alos, O. Mazet and D. Nualart) Alos-Mazet-Nualart