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Math
671 — Fall 2001
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| Instructor: | E. B. Dynkin |
| Time: | TR 10:10–11:25 |
| Room: | Malott 206 |
Probability spaces,
Extension theorems,
Measurable mappings- Random variables,
$\pi-\lambda$ and the Multiplicative systems theorems,
Review of the Lebesgue theory, Fubini's and the Radon-Nikodym theorems,
Conditioning, Independence, Kolmogorov's 0-1 law, The Borel-Cantelly lemma, Kolmogorov's inequality, Series with independent terms,
Strong laws of large numbers, Weak laws of large numbers,
Laplace transform and generating functions, Branching processes,
Fourier transform-characteristic functions, Inversion formula, Central limit theorem (the Lindeberg-Feller conditions), Infinitely divisible distributions and the corresponding limit theorems, Stable distributions,
Poisson point process, White noise, Multivariant normal distribution.
Last modified: April 7, 2003
