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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
An Introduction to Probability and Stochastic Processes

An Introduction to Probability and Stochastic Processes

Berger, Marc A.

Paperback

Series: Springer Texts in Statistics

Probability & Statistics

ISBN10: 1461276438
ISBN13: 9781461276432
Publisher: Springer Pg
Published: Sep 16 2011
Pages: 205
Weight: 0.74
Height: 0.50 Width: 6.14 Depth: 9.21
Language: English
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.

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