| 期刊全称 | An Introduction to Probability and Stochastic Processes | | 影响因子2023 | Marc A. Berger | | 视频video | | | 学科分类 | Springer Texts in Statistics | | 图书封面 |  | | 影响因子 | 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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发表于 2025-3-21 16:49:10
