Local times and excursion theory for Brownian motion : a tale of Wiener and Itô measures
- Ju-Yi Yen, Marc Yor.
- Cham [Switzerland] : Springer, c2013.
- Physical description
- ix, 135 p. : ill. (some col.) ; 24 cm.
- Lecture notes in mathematics (Springer-Verlag) 2088.
Science Library (Li and Ma)
|Shelved by Series title V.2088||Unknown|
- Includes bibliographical references and index.
- Part I: Local Times of Continuous Semimartingales. The Existence and Regularity of Semimartingale Local Times
- Lévy's Representation of Reflecting BM and Pitman's Representation of BES(3)
- Paul Lévy's Arcsine Laws
- Part II: Excursion Theory for Brownian Paths. Brownian Excursion Theory: A First Approach
- Two Descriptions of n: Itô's and Williams'
- A Simple Path Decomposition of Brownian Motion Around Time t = 1
- The Laws of, and Conditioning with Respect to, Last Passage Times
- Integral Representations Relating W and n
- Part III: Some Applications of Excursion Theory. The Feynman-Kac Formula and Excursion Theory
- Some Identities in Law.
- Publisher's Summary
- This monograph discusses the existence and regularity properties of local times associated to a continuous semimartingale, as well as excursion theory for Brownian paths. Realizations of Brownian excursion processes may be translated in terms of the realizations of a Wiener process under certain conditions. With this aim in mind, the monograph presents applications to topics which are not usually treated with the same tools, e.g.: arc sine law, laws of functionals of Brownian motion, and the Feynman-Kac formula.
(source: Nielsen Book Data)9783319012698 20160612
- Publication date
- Lecture notes in mathematics, 0075-8434 ; 2088
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