Everything can change without notice at any moment…

 

Theory of Probability, Part II (MATH 507b)
Spring 2021
Class number  39716R

 

Math 507b in Spring 2021 semester: Key dates

 January 15: First day of classes

 January 18: MLK Day, no class

 February 15: Presidents Day, no class

 March 12: Wellness Day, no class

 March 19: Midterm exam

 April 7: Wellness Day, no class

 April 30: Wellness Day, no class

 May 5: Final exam

 

Instructor: Sergey Lototsky.
Office: KAP 248D.
Phone: 213 740 2389
E-mail: lototsky usc edu.

URL: https://dornsife.usc.edu/sergey-lototsky/

Lectures MWF 1-1:50pm.

Office Hours  about 30 min before and after most lectures
Appointments at other time are welcome.

Course goal   to learn the content of the main reference.

Course objective   to prepare for whatever might be coming next, especially in continuous time.

Course work  homework assignments, in-class presentation, final exam.

Official grading scheme   40% homework assignments, 20% Midterm,  40% final exam.

Main reference   Chapters 4-8 in the book Probability: Theory and Examples, 4th edition, by R. Durrett, Cambridge University Press, 2010.

Supplemental reference   Probability by A. Shiryaev, 2nd edition (Springer, 1996), especially Chapters II, V, VII, and VIII.

Homework problems (do at least one per week)

Some other references

R. Ash. Probability and Measure Theory, 2nd edition, Academic Press, 2000.

K. Athreya, S. Lahiri. Measure Theory and Probability Theory, Academic Press, 2006.

Y. Chow, H. Teichner. Probability Theory, Springer, 1978-1997.

Kai Lai Chung. A Course in Probability Theory, Academic Press, 1968-2001.

C. Dellacherie, P.-A. Meyer. Probabilities and Potential.  North-Holland Publishing Co.,  1988.

A. Gut. Probability: A Graduate Course, Springer, 2005.

R. Dudley. Real Analysis and Probability, Cambridge University Press, 2004.

O. Kallenberg. Foundations of Modern Probability, Springer, 1997-2002.

D. Khoshnevisan. Probability, American Mathematical Society, 2007.

A. Klenke. Probability Theory, Springer, 2008-2014.

G. Lawler. Introduction to Stochastic Processes, Chapman and Hall, 1995.

M. Loeve. Probability Theory (Two Volumes), Springer, 1963-1978.

H. Tucker. A Graduate Course in Probability, Academic Press, 1967.

Ya. Sinai, L. Korallov. Theory of Probability and Random Processes, 2nd edition, Springer, 2007.

D. Williams. Probability with Martingales, Cambridge University Press, 1991.

 

Supplemental material

My notes:

Other notes:
Some martingale inequalities [two pages from Shiryaev]

How to generate symmetric alpha-stable random variables [a research paper]

Donsker’s Theorem [lecture notes by Davar Khoshnevisan]

Probability distributions [a survey paper]

Benford’s law [a survey paper]

Size-biasing [a survey paper]

Borwien integrals and random walk [for fun]

A musical challenge: what music piece contains this?