18.676. Stochastic Calculus.

Spring 2022, MW 11:00-12:30 in 2-139.

All announcements and course materials will be posted on the 18.676 Canvas page.
Some general course information is below.

Prerequisite: 18.675.

Instructor: Nike Sun (nsun at ##).
TA: Gonzalo Cao Labora (gcaol at ##).
## = mit dot edu. Please include "18.676" in the subject line of all emails.
All office hours will be announced on Canvas (see the calendar).
To find a study group, see psetpartners.mit.edu.

03/16/2022 (Wednesday) exam 1 will be held during the lecture time slot.
05/09/2022 (Monday) exam 2 will be held during the lecture time slot.

REFERENCES. References marked * are available for free electronically through libraries.mit.edu.
Main references for this class:
*[online] J.-F. Le Gall, Brownian Motion, Martingales, and Stochastic Calculus. Springer, 2016.
*[online] O. Kallenberg, Foundations of Modern Probability, 2nd ed., Springer, 2002.
Additional references for stochastic calculus:
*[online] I. Karatzas and S. E. Shreve, Brownian Motion and Stochastic Calculus, Springer, 1998.
*[online] D. Revuz and M. Yor, Continuous Martingales and Brownian Motion, Springer, 1999.
*[online] J. M. Steele, Stochastic Calculus and Financial Applications. Springer, 2001.
*[online] D. Stroock, Elements of Stochastic Calculus and Analysis. Springer, 2018.
[online] G. Lawler, Stochastic Calculus: An Introduction with Applications (book draft).
[online] N. Berestycki, lecture notes for stochastic calculus.
[online] D. Stroock, lecture notes for 18.676, compiled by Sinho Chewi.
[online] J. Pitman and M. Yor, "A guide to Brownian motion and related stochastic processes."
Additional references for general probability and analysis:
*[online] E. H. Lieb and M. Loss, Analysis, AMS, 2001.
*[online] R. Durett, Probability: Theory and Examples, Cambridge UP, 2019.
[online] A. Dembo, lecture notes for Stanford Math 230 / Stat 310.
[online] D. Aldous, lecture notes for Berkeley Math 218A / Stat 205A, compiled by Sinho Chewi.