Cornell Math - MATH 671, Fall 2005

MATH 671: Probability Theory (Fall 2005)

Instructor: Eugene Dynkin

Meeting Time & Room

• Probability spaces,
• Extension theorems,
• Measurable mappings- Random variables,
• π – λ 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, 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.