Some Aspects of Brownian Motion: Part II: Some Recent Martingale Problems Marc Yor

ISBN: 9783764357177

Published: March 20th 1997

Paperback

164 pages


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Some Aspects of Brownian Motion: Part II: Some Recent Martingale Problems  by  Marc Yor

Some Aspects of Brownian Motion: Part II: Some Recent Martingale Problems by Marc Yor
March 20th 1997 | Paperback | PDF, EPUB, FB2, DjVu, talking book, mp3, ZIP | 164 pages | ISBN: 9783764357177 | 10.46 Mb

The following notes represent approximately the second half of the lectures I gave in the Nachdiplomvorlesung, in ETH, Zurich, between October 1991 and February 1992, together with the contents of six additional lectures I gave in ETH, in NovemberMoreThe following notes represent approximately the second half of the lectures I gave in the Nachdiplomvorlesung, in ETH, Zurich, between October 1991 and February 1992, together with the contents of six additional lectures I gave in ETH, in November and December 1993.

Part I, the elder brother of the present book [Part II], aimed at the computation, as explicitly as possible, of a number of interesting functionals of Brownian motion. It may be natural that Part II, the younger brother, looks more into the main technique with which Part I was working, namely: martingales and stochastic calculus. As F. Knight writes, in a review article on Part I, in which research on Brownian motion is compared to gold mining: In the days of P.

Levy, and even as late as the theorems of Ray and Knight (1963), it was possible for the practiced eye to pick up valuable reward without the aid of much technology . . . Thereafter, however, the rewards are increasingly achieved by the application of high technology. Although one might argue whether this golden age is really foregone, and discuss the height of the technology involved, this quotation is closely related to the main motivations of Part II: this technology, which includes stochastic calculus for general discontinuous semi-martingales, enlargement of filtrations, .

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