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Titlebook: An Introduction to Probability and Stochastic Processes; Marc A. Berger Textbook 1993 Springer-Verlag New York, Inc. 1993 Ergodic theory.L

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期刊全稱An Introduction to Probability and Stochastic Processes
影響因子2023Marc A. Berger
視頻videohttp://file.papertrans.cn/156/155432/155432.mp4
學(xué)科分類Springer Texts in Statistics
圖書封面Titlebook: An Introduction to Probability and Stochastic Processes;  Marc A. Berger Textbook 1993 Springer-Verlag New York, Inc. 1993 Ergodic theory.L
影響因子These notes were written as a result of my having taught a "nonmeasure theoretic" course in probability and stochastic processes a few times at the Weizmann Institute in Israel. I have tried to follow two principles. The first is to prove things "probabilistically" whenever possible without recourse to other branches of mathematics and in a notation that is as "probabilistic" as possible. Thus, for example, the asymptotics of pn for large n, where P is a stochastic matrix, is developed in Section V by using passage probabilities and hitting times rather than, say, pulling in Perron- Frobenius theory or spectral analysis. Similarly in Section II the joint normal distribution is studied through conditional expectation rather than quadratic forms. The second principle I have tried to follow is to only prove results in their simple forms and to try to eliminate any minor technical com- putations from proofs, so as to expose the most important steps. Steps in proofs or derivations that involve algebra or basic calculus are not shown; only steps involving, say, the use of independence or a dominated convergence argument or an assumptjon in a theorem are displayed. For example, in proving
Pindex Textbook 1993
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,Markov Chains—Passage Phenomena,t and Stone (Ref. [28]), and is presented here with their kind permission. I have adopted their notation and style, because I feel it is the best way to introduce Markov chains in the spirit of these notes—namely, an approach which combines intuition (of the dynamics) with probabilistic reasoning. T
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Markov Jump Processes,as two ingredients. There are random . 0 < τ. < τ. < … < τ. < … when the process jumps away from the state it is at, and there are . Q. that govern the transitions at these jump times. The process {X(.): . ≥ 0 } itself has piecewise constant paths, which we can take to be right-continuous
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Textbook 1993ions from proofs, so as to expose the most important steps. Steps in proofs or derivations that involve algebra or basic calculus are not shown; only steps involving, say, the use of independence or a dominated convergence argument or an assumptjon in a theorem are displayed. For example, in proving
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