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Dynamical Theories of Brownian Motion (Mathematical Notes) by Edward Nelson

Dynamical Theories of Brownian Motion (Mathematical Notes) by Edward Nelson
Publisher: Princeton University Press; Second edition, 2001 edition (February 1, 1967) | ISBN: 0691079501 | Pages: 148 | DJVU | 1.49 MB

These are the notes for the second term of a year course on stochastic processes. The audience was familiar with Markoff processes, martingales, the detailed nature of the sample paths of the Wiener process, and measure theory on the space of sample paths.

After some historical and elementary material in chapters 1-8, we discuss the Ornstein-Uhlenbeck theory of Brownian motion in chapters 9-10, showing that the Einstein-Smoluchowski theory is in a rigorous and strong sense the limiting theory for infinite friction. The results of the long chapter 11 are not used in the following, except for the concepts of mean forward velocity, mean backward velocity, and mean acceleration. The rest of the notes deal with probability theory in quantum mechanics and in the alternative stochastic theory due to Imre Fenyes and others.

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