| An Introduction to Probability and Stochastic Processes Softcover Repri Edition Contributor(s): Berger, Marc A. (Author) |
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ISBN: 1461276438 ISBN-13: 9781461276432 Publisher: Springer OUR PRICE: $52.24 Product Type: Paperback - Other Formats Published: September 2011 |
| Additional Information |
| BISAC Categories: - Mathematics | Probability & Statistics - General |
| Dewey: 519.2 |
| Series: Springer Texts in Statistics |
| Physical Information: 0.5" H x 6.14" W x 9.21" (0.74 lbs) 205 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |
