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## ST779 - Measure Theory and Advanced Probability

- Prerequisites: MA425 or MA 511 or equivalent, and ST701 (or equivalent).
- Term & Frequency: Every Fall
- Student Audience: PhD students in Statistics and related fields
- Credit: 3 credits
- Recent Texts: A Probabilty Path by S. Resnick (Birkhauser, 1999) or Measure Theory & Probability Theory by K. Athreya and S. Lahiri (Springer, 2006)
- Recent Instructors: Subhashis Ghoshal, Soumendra Lahiri
- Background and Goals: This course is designed to train graduate students on theoretical foundations of probability theory, integration techniques and properties of random variables and their collections. Techniques learned from this course play important roles in statistical inference and all branches of mathematical statistics. Homework will involve application of the theorems taught in the course in more concrete contexts.\
- Content: Classes of events, random variables, probability measures, integration and expectation, inequalities, Lp-spaces, product spaces, independence, zero-one laws, convergence notions, characteristic function, simplest limit theorems, absolute continuity, conditional expectation and conditional probability, martingale theory, applications of martingale techniques in limit theorems.
- Alternatives: MA/ST747 covers many overlapping topics, but is not generally offered
- Subsequent Courses: ST 790, Asymptotic Statistics, among other things, covers weak convergence and empirical process theory that can be regarded as follow up.

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