{"id":1042,"date":"2023-06-25T19:18:38","date_gmt":"2023-06-26T02:18:38","guid":{"rendered":"https:\/\/dornsife.usc.edu\/sergey-lototsky\/?page_id=1042"},"modified":"2025-08-05T11:13:46","modified_gmt":"2025-08-05T18:13:46","slug":"math-507b-spring-2021","status":"publish","type":"page","link":"https:\/\/dornsife.usc.edu\/sergey-lototsky\/math-507b-spring-2021\/","title":{"rendered":"Math 507b: Theory of Probability, Spring 2021"},"content":{"rendered":"\n\n \n \n\n\n\n\n\n\n\n
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Everything can change without notice at any moment…<\/p>\n

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Theory of Probability, Part II (MATH 507b)
\nSpring 2021
\nClass number\u00a0 39716R<\/h1>\n

 <\/p>\n

Math 507b in Spring 2021 semester: Key dates <\/span><\/h3>\n

\u00a0January 15: First day of classes
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\u00a0January 18: MLK Day, no class
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\u00a0February 15: Presidents Day, no class
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\u00a0March 12: Wellness Day, no class
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\u00a0March 19: Midterm exam
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\u00a0April 7: Wellness Day, no class
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\u00a0April 30: Wellness Day, no class<\/span><\/p>\n

\u00a0May 5: Final exam
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Instructor: <\/strong> Sergey Lototsky. <\/a>
\n Office:<\/strong> KAP 248D.
\n Phone:<\/strong> 213 740 2389
\n E-mail:<\/strong> lototsky usc edu.<\/h2>\n

URL:\u00a0https:\/\/dornsife.usc.edu\/sergey-lototsky\/<\/strong><\/p>\n

Lectures<\/strong> MWF 1-1:50pm.<\/p>\n

Office Hours<\/strong>\u00a0 about 30 min before and after most lectures
\nAppointments at other time are welcome.<\/p>\n

Course goal \u00a0 <\/strong>to learn the content of the main reference.
\n<\/strong><\/p>\n

Course objective\u00a0\u00a0 <\/strong>to prepare for whatever might be coming next, especially in continuous time.
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Course work\u00a0<\/strong> homework assignments, in-class presentation, final exam.<\/p>\n

Official grading scheme \u00a0 <\/strong>40% homework assignments, 20% Midterm,\u00a0 40% final exam.<\/p>\n

Main reference\u00a0<\/strong>\u00a0 Chapters 4-8 in the book Probability: Theory and Examples<\/em>, 4th edition, by R. Durrett, Cambridge University Press, 2010.<\/p>\n

Supplemental reference<\/strong>\u00a0\u00a0 Probability<\/em> by A. Shiryaev, 2nd edition (Springer, 1996), especially Chapters II, V, VII, and VIII.<\/p>\n

Homework problems<\/a> (do at least one per week)<\/h3>\n

Some other references<\/strong><\/p>\n

R. Ash. Probability and Measure Theory, 2nd edition, Academic Press, 2000.<\/p>\n

K. Athreya, S. Lahiri. Measure Theory and Probability Theory, Academic Press, 2006.<\/p>\n

Y. Chow, H. Teichner. Probability Theory, Springer, 1978-1997.<\/p>\n

Kai Lai Chung. A Course in Probability Theory, Academic Press, 1968-2001.<\/p>\n

C. Dellacherie, P.-A. Meyer. Probabilities and Potential.\u00a0<\/span> North-Holland Publishing Co.,\u00a0<\/em> 1988.<\/p>\n

A. Gut. Probability: A Graduate Course, Springer, 2005.<\/p>\n

R. Dudley. Real Analysis and Probability, Cambridge University Press, 2004.<\/p>\n

O. Kallenberg. Foundations of Modern Probability, Springer, 1997-2002.<\/p>\n

D. Khoshnevisan. Probability, American Mathematical Society, 2007.<\/p>\n

A. Klenke. Probability Theory, Springer, 2008-2014.<\/p>\n

G. Lawler. Introduction to Stochastic Processes, Chapman and Hall, 1995.<\/p>\n

M. Loeve. Probability Theory (Two Volumes), Springer, 1963-1978.<\/p>\n

H. Tucker. A Graduate Course in Probability, Academic Press, 1967.<\/p>\n

Ya. Sinai, L. Korallov. Theory of Probability and Random Processes, 2nd edition, Springer, 2007.<\/p>\n

D. Williams. Probability with Martingales, Cambridge University Press, 1991.<\/p>\n

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Supplemental material<\/strong><\/p>\n

My notes:
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