The Annals of Probability

Slow Points in the Support of Historical Brownian Motion

John Verzani

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Abstract

A slow point from the left for Brownian motion is a time during a given interval for which the oscillations of the path immediately to the left of this time are smaller than the typical ones, that is, those given by the local LIL. These slow points occur at random times during a given interval. For historical super-Brownian motion, the support at a fixed time contains an infinite collection of paths. This paper makes use of a branching process description of the support to investigate the slowness of these paths at the fixed time. The upper function found is the same as that found for slow points in the Brownian motion case.

Article information

Source
Ann. Probab., Volume 23, Number 1 (1995), 56-70.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176988376

Digital Object Identifier
doi:10.1214/aop/1176988376

Mathematical Reviews number (MathSciNet)
MR1330760

Zentralblatt MATH identifier
0841.60067

JSTOR
links.jstor.org

Subjects
Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60G17: Sample path properties

Keywords
Branching Brownian motion superprocesses path properties measure-valued diffusions slow points fast points

Citation

Verzani, John. Slow Points in the Support of Historical Brownian Motion. Ann. Probab. 23 (1995), no. 1, 56--70. doi:10.1214/aop/1176988376. https://projecteuclid.org/euclid.aop/1176988376


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