The course is on Canvas
Homework
Homework #1 – Review of Expectation and Conditional Expectation
Homework #2 – Review of Discrete-time Martingales
Homework #3 – Review of Brownian Motion
Homework #4 – Stochastic Integration and Ito’s formula
Lecture Notes
First week’s Lecture Notes: Notes-1, Notes-2, Notes-3, Notes-4, Notes-5, Notes-6, Notes-7
Martingales and Uniform Integrability: Notes
Brownian Motion: Notes
Syllabus
Time and Location
M-W-F Period 5 (11:45 AM – 12:35 PM), ONLINE (Zoom link available in Canvas)
Classes will be live and recorded. Recording will be available for viewing in Canvas.
Office Hours
By appointment
Textbook
There is no required text, but the following textbooks are suggested:
- G. F. Lawler, Stochastic Calculus: An Introduction with Applications (PDF available on Prof. Lawler’s website).
- P. E. Protter, Stochastic Integration and Differential Equations, Springer.
- R. Durrett, Probability: Theory and Examples, 5th edition (PDF available on Prof. Durrett’s website)
- P. Morters and Y. Peres, Brownian Motion, Cambridge University Press (PDF available on Prof. Morters’ website)
Final Exam Date
Friday, December 18 (12/18/2020) at 12:30 PM — 2:30 PM
Scope of the course
The aim of the course is to provide students with strong foundations in the area of probability theory. At the end of the course, students will be acquainted with the language of probability and will gain sufficient experience to successfully apply probabilistic tools to most areas of pure and applied sciences.
The course is intended for graduate students as part of their PhD requirement, and for students considering studying probability theory at a research level.
Prerequisite
MAP 6472-6473 — Probability and Potential Theory
Topics Covered
Topics include continuous time Martingales, Brownian motion, Stochastic integral, Itô calculus, Stochastic differential equations. Below is the weekly schedule:
W1: Review of Lebesgue integral.
W2: Review of conditional expectation.
W3: Continuous time martingales.
W4: Backward martingale and Lévy’s downward theorem.
W5: Review of Brownian motion.
W6: Review of Riemann integral.
W7: Construction of stochastic integral.
W8: Properties of the stochastic integral.
W9: Itô calculus.
W10: Stochastic differential equations.
W11: Ornstein-Ulhenbeck process, Black-Scholes model in finance.
W12: Simulation.
W13-W14: Change of measure, Girsanov theorem.
Process for Final Exam (Online):
Date and Time: Friday, December 18 (12/18/2020) at 12:30 PM – 2:30 PM.
On Friday, December 18 at 12:30 PM, the final exam will be posted on Canvas. You have 2 hours to complete the exam. Then, you will need to scan or take a picture of your test, and submit it via Canvas (pdf or jpeg file only).
The deadline to submit your test is 3 PM on Friday, December 18. Canvas will stamp your submission. Late submission is not accepted.
MAKE SURE YOUR FILE IS READABLE BEFORE SUBMISSION.
I trust that you will not seek external help. Please keep in mind the Honor Code at the
University of Florida, the following pledge is either required or implied:
“On my honor, I have neither given nor received unauthorized aid in doing this
assignment”.
Take Home Exam #2 – Average = 20.5 (out of 25)
Take Home Exam #1 – Average = 21.35 (out of 25)
[Individual grades are available on Canvas]