Course Archives Theoretical Statistics and Mathematics Unit | |||||||||||||
Course: Measure Theoretic Probability Instructor: Yogeshwaran D Room: G25 Time: Currently offered Level: Postgraduate |
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Syllabus Past Exams Syllabus: Measure and Integration: Monotone Class Theorem, Probability and Measures, Construction of Lebesgue measure, Integration, Fatou Lemma, Monotone and DominatedConvergence Theorems, Radon- Nikodym theorem, product measures, Fubinis theorem. Probability: (If needed, a quick review of concepts and results (without proof) from basic Discrete and Continuous Probabilty.) Distribution Functions of Probabilty Measures on R, Borel-Cantelli Lemma, Weak and Strong Laws of Large Numbers in i.i.d. case, various Modes of Convergende, Characteristic Functions, Uniqueness/Inversion/Levy Continuity Theorems, Proof of the Central Limit Theorem for i.i.d. case with Finite Variance. Suggested Texts: 1. W. Rudin, Real and complex analysis, McGraw-Hill Book Co. (1987). 2. P. Billingsley, Probability and measure, John Wiley (1995). 3. K. R. Parthasarathy, Introduction to probability and measure, TRIM (33), Hindustan Book Agency (2005). 4. J. Nevue, Mathematical foundations of the calculus of probability, Holden- Day (1965). 5. I. K. Rana, An introduction to measure and integration, Narosa Publishing House (1997). Evaluation:
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Midterm
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