{"id":1062,"date":"2023-06-25T19:21:21","date_gmt":"2023-06-26T02:21:21","guid":{"rendered":"https:\/\/dornsife.usc.edu\/sergey-lototsky\/?page_id=1062"},"modified":"2023-06-25T19:21:23","modified_gmt":"2023-06-26T02:21:23","slug":"math-605-fall-2019","status":"publish","type":"page","link":"https:\/\/dornsife.usc.edu\/sergey-lototsky\/math-605-fall-2019\/","title":{"rendered":"Math 605: Topics in Probability, Fall 2019"},"content":{"rendered":"\n\n \n \n\n\n\n\n\n\n\n
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 <\/p>\n

MATH 605, Fall 2019.
\nTopics in Probability (39788R)
\nNumerical Methods in Stochastic Analysis
\n Class meetings: MW 4:30-5:50pm, KAP 245
\n<\/span><\/h1>\n

 <\/p>\n

Information on this and linked pages changes frequently.<\/h2>\n

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

Office Hours: MWF 11-11:50am in KAP 248D
\nWalk-ins and appointments at other time are welcome.<\/p>\n

Course objective <\/strong>To learn the main problems, tools, and algorithms related to Monte Carlo and similar methods.<\/p>\n

Course work <\/strong>Class participation, homework assignments, final presentation.<\/p>\n

Official grading scheme <\/strong>20% class participation, 40% homework assignments, 40% final presentation.<\/p>\n

Main reference <\/strong> Stochastic Simulation: Algorithms and Analysis by S. Asmussen and P. W. Glynn, published by Springer in the series “Stochastic Modeling and Applied Probability”, vol. 57, 2007.<\/p>\n

Class announcement flyer<\/a><\/p>\n

Class notes<\/a> (my version, frequently updated)
\nI expect you to (1) do the problems, (2) think about the questions, (3) have a one-sentence description of the each of the key ideas and “other points”, (4) remember some of the “random bits and pieces”.<\/p>\n

Our Progress <\/strong><\/p>\n

August 26\u00a0\u00a0 \u00a0<\/strong>\u00a0\u00a0 Generation of Uniform(0,1) random variables; discrete distributions from Uniform(0,1).<\/p>\n

August 28\u00a0 \u00a0\u00a0 \u00a0 <\/strong>Randomness and related ideas.<\/p>\n

September 2 \u00a0<\/strong> Labor Day, no class.<\/p>\n

September 4\u00a0\u00a0 <\/strong>Generation of continuous random variables; infinite divisibility, stability, and related notions.<\/p>\n

September 9<\/strong>\u00a0 Variance reduction.<\/p>\n

September 11<\/strong> “Random” bits and pieces related to generation of random objects.<\/p>\n

September 16<\/strong> Markov chains, regeneration identity,\u00a0 and the Propp-Wilson algorithm.<\/p>\n

September 18<\/strong> Rare events and importance sampling.<\/p>\n

September 23<\/strong> Siegmund’s algorithm.<\/p>\n

September 25<\/strong> Standard Brownian motion.<\/p>\n

September 30<\/strong> SODEs: Existence and uniqueness of solution<\/p>\n

October 2<\/strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 SODEs: Euler-Maryama and Milstein schemes<\/p>\n

October 7<\/strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Stochastic Approximation: Robbins-Monro et al.<\/p>\n

October 9<\/strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Stochastic Approximation: estimation with heavy-tailed noise<\/p>\n

October 14<\/strong>\u00a0\u00a0\u00a0\u00a0 MCMC: Metropolis-Hastings<\/p>\n

October 16 \u00a0 \u00a0 \u00a0<\/strong>MCMC: Langevin and beyond<\/p>\n

October 21 \u00a0 \u00a0 \u00a0<\/strong>Orthogonal polynomials: an overview<\/p>\n

October 23 \u00a0 \u00a0 \u00a0<\/strong>Polynomial Chaos: Gaussian bi-linear case<\/p>\n

October 28 \u00a0 \u00a0 \u00a0<\/strong>Polynomial Chaos: Non-linear case<\/p>\n

October 30 \u00a0 \u00a0 \u00a0<\/strong>Orthogonal polynomials: Levy-Sheffer and Levy-Meixner systems<\/p>\n

Novermber 4 and 6 <\/strong>Select topics in asymptotic analysis<\/p>\n

Student presentations begin.<\/strong><\/p>\n

November 11 \u00a0<\/strong>John on extensions and analysis of the Metropolis-Hastings algorithm<\/p>\n

November 13 \u00a0<\/strong>Maria on statistical approach to inverse problems for partial differntial equations<\/p>\n

November 18 <\/strong>Austin on optimal control approach to the Kelly criterion<\/p>\n

November 20 <\/strong>Apoorva on importance sampling and the random Lorenz system<\/p>\n

November 25\u00a0<\/strong>Ujan on non-centeral limit theorems for martingales<\/p>\n

November 27<\/strong> Thanksgiving Break, no class<\/p>\n

December 2<\/strong>\u00a0\u00a0\u00a0 Anna on generating random logic circuits on a quantum computer<\/p>\n

December 4\u00a0<\/strong>\u00a0\u00a0 Lernik on non-parametric inference via optimiziation in the space of measures<\/p>\n

 <\/p>\n

Supplemental material <\/strong>
\n About Buffon’s needle <\/a> and some further reading on Lazzarini’s experiment <\/a> and on a higer-dimensional application in biology <\/a>
\n The review of the “Stochastic Simulation” book from MathSciNet <\/a><\/p>\n

\n

USC Math Department Homepage<\/a><\/p>\n

\n\n\n\n<\/div>\n\n\n <\/div><\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":282,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"footnotes":""},"class_list":["post-1062","page","type-page","status-publish","hentry"],"acf":[],"yoast_head":"\nMath 605: Topics in Probability, Fall 2019 - Sergey Lototsky<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/dornsife.usc.edu\/sergey-lototsky\/math-605-fall-2019\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Math 605: Topics in Probability, Fall 2019 - Sergey Lototsky\" \/>\n<meta property=\"og:url\" content=\"https:\/\/dornsife.usc.edu\/sergey-lototsky\/math-605-fall-2019\/\" \/>\n<meta property=\"og:site_name\" content=\"Sergey Lototsky\" \/>\n<meta property=\"article:modified_time\" content=\"2023-06-26T02:21:23+00:00\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/dornsife.usc.edu\/sergey-lototsky\/math-605-fall-2019\/\",\"url\":\"https:\/\/dornsife.usc.edu\/sergey-lototsky\/math-605-fall-2019\/\",\"name\":\"Math 605: Topics in Probability, Fall 2019 - 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