18.676. Stochastic Calculus.

Spring 2021, MW 11:00-12:30 (virtual).

All announcements and course materials will be posted on the 18.676 Canvas page. To attend lectures, go to the Zoom section on the Canvas page, and click Join. Some general course information is below.

Prerequisite: 18.675.

Instructor: Nike Sun (nsun at ##).
TA: Matthew Nicoletti (mnicolet 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).

TEXTBOOKS. References marked * are available for free electronically through libraries.mit.edu.
Main reference for this class:
*[online] J.-F. Le Gall, Brownian Motion, Martingales, and Stochastic Calculus. Springer, 2016.
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.
*[online] O. Kallenberg, Foundations of Modern Probability, 2nd ed., Springer, 2002.

GRADING. Homework (60%), exam 1 (18%), exam 2 (18%), class participation (4%).
To find a study group, see psetpartners.mit.edu.

04/07 (Wednesday) exam 1 will be held online, 6:00pm to 8:30pm Boston time.
05/19 (Wednesday) exam 2 will be held online, 6:00pm to 8:30pm Boston time.