Statistics 205A, Fall 2002. Jim Pitman

1 Lecture Notes

Macros .tex file
Lecture 0. Notation. .tex file .ps file .pdf file
Lecture 1. Probability Spaces, Dynkin's pi-lambda theorem.
Lecture 2. Random variables and their distributions.
Lecture 3. Expectation, MCT, DCT, Change of variable.
Lecture 4. Moments, inequalities, joint laws,
Lecture 5. Independence, Fubini's theorem, and the weak law of large numbers. .tex file .ps file .pdf file
Lecture 6. Almost sure convergence and the Borel-Cantelli lemmas. .tex file .ps file .pdf file
Lecture 7. Almost sure limits for sums of independent random variables. .tex file .ps file .pdf file
Lecture 8. Basic L² convergence theorem and Kolmogorov's law of large numbers .tex file .ps file .pdf file
Lecture 9. Weak convergence: basic facts
Lectures 10-11. Lindeberg's CLT .tex file .ps file .pdf file
Lecture 12. Characteristic Functions .ps file .pdf file
Lecture 13. The inversion formula .ps file .pdf file
Lecture 14. Continuity theorem for characteristic functions .ps file .pdf file Note: .tex and .eps files are in directory lecture14
Lectures 15-17. Conditioning. .tex file .ps file .pdf file Note: section numbering should be changed in files.
Lecture 18. Stopping times and Martingales .tex file .ps file .pdf file
Lecture 19. Doob's max ineq. Convergence. Dubins ineq.
Lecture 20. Uniform integrability, Backwards MG, Hewitt Savage 0-1 law
Lecture 21. Conditional Independence, Exchangeability, de Finetti's theorem.
Lecture 22. Applications of de Finetti, Polya's urn
Lectures 23-24. Recurrence and Transience of Random Walks .tex file .ps file .pdf file
Lecture 25. Stochastic Processes. The Markov property.
Lecture 26. Processes with independent increments .tex file .ps file .pdf file
Lecture 27. Poisson point processes .tex file .ps file .pdf file

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On 23 Jan 2003, 18:42.