Probability: A Survey of the Mathematical TheoryJohn Wiley & Sons, 20 вер. 2011 р. - 208 стор. The brand new edition of this classic text--with more exercises andeasier to use than ever Like the first edition, this new version ofLamperti's classic text succeeds in making this fascinating area ofmathematics accessible to readers who have limited knowledge ofmeasure theory and only some familiarity with elementaryprobability. Streamlined for even greater clarity and with moreexercises to help develop and reinforce skills, Probability isideal for graduate and advanced undergraduate students--both in andout of the classroom. Probability covers: * Probability spaces, random variables, and other fundamentalconcepts * Laws of large numbers and random series, including the Law of theIterated Logarithm * Characteristic functions, limiting distributions for sums andmaxima, and the "Central Limit Problem" * The Brownian Motion process |
Зміст
A Survey of the Mathematical Theory 1 Foundations | 1 |
A Survey of the Mathematical Theory 2 Laws of Large Numbers and Random Series | 31 |
A Survey of the Mathematical Theory 3 Limiting Distributions and the Central Limit Problem | 71 |
A Survey of the Mathematical Theory 4 The Brownian Motion Process | 131 |
A Survey of the Mathematical Theory Appendix Essentials of Measure Theory | 175 |
A Survey of the Mathematical Theory Bibliography | 181 |
| 183 | |
A Survey of the Mathematical Theory List of Series Titles | 191 |
Інші видання - Показати все
Probability: A Survey of the Mathematical Theory John W. Lamperti Обмежений попередній перегляд - 1996 |
Загальні терміни та фрази
Analysis apply assume Bernoulli trials Borel sets Borel-Cantelli lemma bounded Brownian motion Brownian motion process characteristic function common distribution conditional expectation constants continuous function converges weakly Corollary countable covariance defined definition denote density difficulty distribution function easy example exists expected value find finishes finite number finite-dimensional distributions first follows Fourier function F holds identically distributed implies independent random variables indicator function inequality infinitely divisible integral interval joint distribution Kolmogorov large numbers law of large Lebesgue measure Lemma lim sup limit theorem limiting distributions linear Markov process matrix means measurable space Methods nonnegative normal distribution o-field obtain partial sums probability measures probability space probability theory Problem proof of Theorem prove random vari rational number Remark result right-hand side satisfies Second Edition Section sequence of independent stable distributions standard normal stochastic process sufficient Suppose symmetric transition function variance vector verified Verify weak convergence