18.676. Stochastic Calculus.

Spring 2020, MW 11:00-12:30 in 2-131. This class is a re-numbering of 18.176.

Prerequisite: 18.675. (The fall 2019 page contains a summary of topics covered.)

Instructor: Nike Sun (nsun at ##), office hours Mondays 1-3pm.
TAs: Morris Ang (angm at ##) and Vishesh Jain (visheshj at ##).
## = mit dot edu. Please include "18.676" in the subject line of all emails.
Homework will be announced and posted on Stellar.

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, 1st ed., Springer, 1997. (In the notes I follow the numbering of the 2nd edition which is not freely available from the library. If you need help finding the corresponding numbering in the first edition, please email me.)

GRADING. Homework (65%), exam 1 (15%), exam 2 (15%), class participation (5%). Note that emergency academic regulations are in effect, so all grades will be PE/NE/IE. The detailed course policy is on Stellar.

KEY DATES. (See also the academic calendar.)
02/17 (Monday) is a holiday; 02/18 (Tuesday) the Monday schedule will be held.
03/12 (Thursday) exam 1 will be held from 6:00pm to 8:30pm (cancelled).
Weeks of 03/16 and 03/23: no classes (MIT emergency closure).
03/30 (Monday) classes resume online.
04/02 (Thursday) exam 1 will be held online from 6:00pm to 8:30pm.
04/20 (Monday) is a holiday.
05/07 (Thursday) exam 2 will be held online from 6:00pm to 8:30pm.
05/11 (Monday) is the last lecture.

Andrew Lin is sharing his class notes as an informal additional resource.