Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

The local time process of a circular Brownian motion

The local time process of a circular Brownian motion Vo1.16 No.1 ACTA MATHEMATICAE APPLICATAE SINICA Jan., 2000 Study Bulletin THE LOCAL TIME PROCESS OF A CIRCULAR BROWNIAN MOTION* XIANG KAINAN (I~:~-~) (Institute of Applied Mathematics, the Chinese Academy of Sciences, Beijing 100080, China) Main Result Let P~ be the distribution of a one-dimensional Brownian motion (Bt, t >_ 0) with drift 6 starting at B0 = 0. A Brownian motion (Bt, t > 0) on a circle of unit circumference can be obtained as Bt = Bt mod 1,-where the circle is identified with [0, 1). The local time process of B is (-~t = ~ ~tr~'+z, 0<u< 1), where Z is the set of integers, and (L~, x e R, t _> 0) zEZ is the usual bicontinuous local time process of B, normalized as occupation density relative to Lebesgue measure. Let C+([0, 1)) be the space of nonnegative continuous paths with domain [0, 1). For a random time T, set LT = (~T, 0 _< u < 1), and view LT as a C+([0, 1)) valued random path. Let Tr be the cover time of the circular Brownian motion, namely, Tr = inf {t; Rt = 1}, where Rt= max Bs- min Bs. 0<s<t 0<8_<t Denote http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

The local time process of a circular Brownian motion

Kainan, Xiang
Acta Mathematicae Applicatae Sinica , Volume 16 (1) – Jul 7, 2007
Download PDF
2 pages

Loading next page...
 
/lp/springer-journals/the-local-time-process-of-a-circular-brownian-motion-Zt5mpNjMGr

References (4)

Publisher
Springer Journals
Copyright
Copyright © 2000 by Science Press
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/BF02670971
Publisher site
See Article on Publisher Site

Abstract

Vo1.16 No.1 ACTA MATHEMATICAE APPLICATAE SINICA Jan., 2000 Study Bulletin THE LOCAL TIME PROCESS OF A CIRCULAR BROWNIAN MOTION* XIANG KAINAN (I~:~-~) (Institute of Applied Mathematics, the Chinese Academy of Sciences, Beijing 100080, China) Main Result Let P~ be the distribution of a one-dimensional Brownian motion (Bt, t >_ 0) with drift 6 starting at B0 = 0. A Brownian motion (Bt, t > 0) on a circle of unit circumference can be obtained as Bt = Bt mod 1,-where the circle is identified with [0, 1). The local time process of B is (-~t = ~ ~tr~'+z, 0<u< 1), where Z is the set of integers, and (L~, x e R, t _> 0) zEZ is the usual bicontinuous local time process of B, normalized as occupation density relative to Lebesgue measure. Let C+([0, 1)) be the space of nonnegative continuous paths with domain [0, 1). For a random time T, set LT = (~T, 0 _< u < 1), and view LT as a C+([0, 1)) valued random path. Let Tr be the cover time of the circular Brownian motion, namely, Tr = inf {t; Rt = 1}, where Rt= max Bs- min Bs. 0<s<t 0<8_<t Denote

Journal

Acta Mathematicae Applicatae Sinica – Springer Journals

Published: Jul 7, 2007

There are no references for this article.