Probability : theory and examples
著者
書誌事項
Probability : theory and examples
（The Duxbury advanced series）
Thomson Brooks/Cole, c2005
3rd ed
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注記
Includes bibliographical references (p. [481]-488) and index
内容説明・目次
内容説明
A useful reference.for those who apply probability to work, PROBABILITY: THEORY AND EXAMPLES focuses attention on examples and results while developing theory.
目次
INTRODUCTORY LECTURE. 1. LAWS OF LARGE NUMBERS. Basic Definitions. Random Variables. Expected Value. Independence. Weak Laws of Large Numbers. Borel-Cantelli Lemmas. Strong Law of Large Numbers. Convergence of Random Series. Large Deviations. 2. CENTRAL LIMIT THEOREMS. The De Moivre-Laplace Theorem. Weak Convergence. Characteristic Functions. Central Limit Theorems. Local Limit Theorems. Poisson Convergence. Stable Laws. Infinitely Divisible Distributions. Limit theorems in Rd. 3. RANDOM WALKS. Stopping Times. Recurrence. Visits to 0, Arcsine Laws. Renewal Theory. 4. MARTINGALES. Conditional Expectation. Martingales, Almost Sure Convergence. Examples. Doob's Inequality, LP Convergence. Uniform Integrability, Convergence in L1 / Backwards Martingales. Optional Stopping Theorems. 5. MARKOV CHAINS. Definitions and Examples. Extensions of the Markov Property. Recurrence and Transience. Stationary Measures. Asymptotic Behavior. General State Space. 6. ERGODIC THEOREMS. Definitions and Examples. Birkhoff's Ergodic Theorem. Recurrence. Mixing. Entropy. A Subadditive Ergodic Theorem. Applications. 7. BROWNIAN MOTION. Definition and Construction. Markov Property, Blumenthal's 0-1 Law. Stopping Times, Strong Markov Property. Maxima and Zeros. Martingales. Donsker's Theorem. CLT's for Dependent Variables. Empirical Distributions, Brownian Bridge. Laws of the Iterated Logarithm. APPENDIX: MEASURE THEORY. REFERENCES. NOTATION. NORMAL TABLE. INDEX.
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