Probability: Theory and ExamplesDuxbury Press, 1996 - 503 páginas Modern and measure-theory based, this text is intended primarily for the first-year graduate course in probability theory. |
Conteúdo
Markov Chains | 5 |
Central Limit Theorems | 79 |
c Prime divisors ErdösKac | 121 |
Direitos autorais | |
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Termos e frases comuns
A₁ B₁ Borel-Cantelli lemma bounded central limit theorem ch.f Chapter characteristic function Chebyshev's inequality compute conclude continuous countable define definition density desired result follows disjoint distribution F distribution function distribution with mean dominated convergence theorem ergodic EX₁ EX² Example EXERCISE finite Fn(x formula Fubini's theorem gives i.i.d. with P(X inequality inf{n integral irreducible large numbers last result law of large Lebesgue measure let Sn Let X1 lim inf lim sup log log Markov chain Markov property martingale N₁ normal distribution o-field observe P(An P(Sn P(X₁ P(Xn permutation Poisson distribution Poisson process probability measure Proof Let random variables random walk recurrent Remark renewal S₁ Section Show simple random walk Sn/n stable law Suppose T₁ trivial var(X variance weak law X₁ Xn,m Y₁