An Introduction to Probability and Stochastic Processes (Springer Texts in Statistics)

Berger, Marc A.

ISBN 10: 1461276438 / ISBN 13: 9781461276432

Published by Springer, 2011

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Bibliographic Details

• Title: An Introduction to Probability and Stochastic Processes (Springer Texts in Statistics)
• Publisher: Springer
• Publication Date: 2011
• Language: English
• ISBN 10: 1461276438
• ISBN 13: 9781461276432
• Binding: Soft cover
• Condition: New

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Synopsis

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 inversion formulas for characteristic functions I omit steps involving evaluation of basic trigonometric integrals and display details only where use is made of Fubini's Theorem or the Dominated Convergence Theorem.