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Local times and excursion theory for Brownian motion : a tale of wiener and itô measures

저자: Ju-Yi Yen; Marc Yor
출판사: Cham, Switzerland : Springer, ©2013.
시리즈: Lecture notes in mathematics (Springer-Verlag), 2088.
판/형식:   전자도서 : 문서 : 영어모든 판과 형식 보기
데이터베이스:WorldCat
요약:
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  더 읽기…
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장르/형태: Electronic books
추가적인 물리적 형식: Printed edition:
자료 유형: 문서, 인터넷 자료
문서 유형 인터넷 자원, 컴퓨터 파일
모든 저자 / 참여자: Ju-Yi Yen; Marc Yor
ISBN: 9783319012704 3319012703
OCLC 번호: 859575095
설명: 1 online resource (ix, 135 pages) : illustrations.
내용: Prerequisites --
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.
일련 제목: Lecture notes in mathematics (Springer-Verlag), 2088.
책임: Ju Yi Yen, Marc Yor.

초록:

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.

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"The lecture notes provide an elementary and brief introduction to local times for continuous semimartingales and excursion theory for Brownian motion. ... The lecture notes are an easily accessible 더 읽기…

 
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