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15.070

Discrete Probability and Stochastic Processes

3-0-9 units · Graduate

Provides an introduction to tools used for probabilistic reasoning in the context of discrete systems and processes. Tools such as the probabilistic method, first and second moment method, martingales, concentration and correlation inequalities, theory of random graphs, weak convergence, random walks and Brownian motion, branching processes, Markov chains, Markov random fields, correlation decay method, isoperimetry, coupling, influences and other basic tools of modern research in probability will be presented. Algorithmic aspects and connections to statistics and machine learning will be emphasized.

Fall 2013 · Advanced Stochastic Processes

This class covers the analysis and modeling of stochastic processes. Topics include measure theoretic probability, martingales, filtration, and stopping theorems, elements of large deviations theory, Brownian motion and reflected Brownian motion, stochastic integration and Ito calculus and functional limit theorems. In addition, the class will go over some applications to finance theory, insurance, queueing and inventory models.

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Prerequisites & course information

Same subject as 6.7720J, 18.619[J] Prereq: 6.3702 , 6.7700[J] , 18.100A , 18.100B , or 18.100Q G (Spring) 3-0-9 units

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