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Quick Facts

Medium Of InstructionsMode Of LearningMode Of Delivery
EnglishSelf StudyVideo Based

Courses and Certificate Fees

Fees InformationsCertificate AvailabilityCertificate Providing Authority
INR 1000yesIIT Kanpur

The fees for the course Measure Theoretic Probability 2 is :

Fees componentsAmount
Exam feesRs. 1,000

The Syllabus

  • Introduction to the course: A review of basic Probability and Measure Theoretic integration
  • Lp spaces (definition, properties as a Banach space, dual space)

  • Independence of Events and Random variables, Borel-Cantelli Lemma (second half)
  • Product measures (construction, integration, Fubini-Tonelli Theorem)
  • Almost sure convergence of sequences of Random variables (definition and examples)

  • Other modes of convergence of sequences of Random variables (convergence in probability, convergence in p-th mean, definition and examples)
  • Relations between various modes of convergence (examples and counter-examples)

  • Properties of various modes of convergence
  • Almost sure convergence of series of Random variables (Kolmogorov’s inequality)

  • Almost sure convergence of series of Random variables – continued (Kolmogorov’s Three series Theorem)
  • Law of Large numbers (Khinchin’s Weak law, Kolmogorov’s Strong law, applications)
  • Characteristic Functions (properties, Inversion formulae)

  • Weak convergence or convergence in distribution (definition and examples)
  • Equivalent conditions or formulations of weak convergence (Helly-Bray Theorem, Portmanteau Lemma, Levy’s Continuity Theorem)

  • Equivalent conditions or formulations of weak convergence – continued
  • Central Limit Theorem (Lindeberg-Levy CLT)

  • Central Limit Theorems (Lindeberg-Feller CLT, Lyapunov CLT)
  • Applications
  • Slutky’s Theorem, Delta Method, Comments on Glivenko-Cantelli Theorem and Berry-Esseen Theorem
  • Conclusion of the course

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