The Annals of Probability

IBM, SIBM and IBS

Robert Adler and John Verzani

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Abstract

We construct a super iterated Brownian motion (SIBM) from a historical version of iterated Brownian motion (IBM) using an iterated Brownian snake (IBS). It is shown that the range of super iterated Brownian motion is qualitatively quite different from that of super Brownian motion in that there are points with explosions in the branching. However, at a fixed time the support of SIBM has an exact Hausdorff measure function that is the same (up to a constant) as that of super Brownian motion at a fixed time.

Article information

Source
Ann. Probab., Volume 28, Number 1 (2000), 462-477.

Dates
First available in Project Euclid: 18 April 2002

Permanent link to this document
https://projecteuclid.org/euclid.aop/1019160126

Digital Object Identifier
doi:10.1214/aop/1019160126

Mathematical Reviews number (MathSciNet)
MR1756012

Zentralblatt MATH identifier
1044.60077

Subjects
Primary: 60G57: Random measures 60G17: Sample path properties
Secondary: 60H15: Stochastic partial differential equations [See also 35R60]

Keywords
Iterated Bownian motion Brownian snake super Brownian motion super iterated Brownian motion iterated Brownian snake exact measure function

Citation

Verzani, John; Adler, Robert. IBM, SIBM and IBS. Ann. Probab. 28 (2000), no. 1, 462--477. doi:10.1214/aop/1019160126. https://projecteuclid.org/euclid.aop/1019160126


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