First Look At Rigorous Probability Theory, A (2nd Edition)World Scientific Publishing Company, 14 de nov. de 2006 - 236 páginas This textbook is an introduction to probability theory using measure theory. It is designed for graduate students in a variety of fields (mathematics, statistics, economics, management, finance, computer science, and engineering) who require a working knowledge of probability theory that is mathematically precise, but without excessive technicalities. The text provides complete proofs of all the essential introductory results. Nevertheless, the treatment is focused and accessible, with the measure theory and mathematical details presented in terms of intuitive probabilistic concepts, rather than as separate, imposing subjects. In this new edition, many exercises and small additional topics have been added and existing ones expanded. The text strikes an appropriate balance, rigorously developing probability theory while avoiding unnecessary detail. |
Conteúdo
| 1 | |
2 Probability triples | 7 |
3 Further probabilistic foundations | 29 |
4 Expected values | 43 |
5 Inequalities and convergence | 57 |
6 Distributions of random variables | 67 |
7 Stochastic processes and gambling games | 73 |
8 Discrete Markov chains | 83 |
11 Characteristic functions | 125 |
12 Decomposition of probability laws | 143 |
13 Conditional probability and expectation | 151 |
14 Martingales | 161 |
15 General stochastic processes | 177 |
A Mathematical Background | 199 |
| 209 | |
| 213 | |
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Termos e frases comuns
absolutely continuous aperiodic Borel-measurable bounded Brownian motion Central Limit Theorem characteristic function coin tossing collection Compute consider continuity of probabilities continuous-time Corollary countable additivity defined definition density discrete disjoint E(Xn equal equation equivalence event Exercise exists expected value finite mean follows Furthermore gambling given Hence Hint implies inequality inf{n infinite integral intentionally left blank interval Intuitively large numbers Lebesgue measure Lemma Let Xn lim inf lim sup limn limn+ linearity Markov chain martingale measure on 0,1 measure theory monotone convergence theorem Mx(s o-algebra P(An P(Xn probability measure probability theory probability triple proof of Theorem Proposition Prove random walk real numbers result satisfied Section summary semialgebra sequence Similarly simple random variable simple symmetric random stationary distribution stochastic process submartingale subsets supn Suppose symmetric random walk transition probabilities Var(X variance weak convergence