IBM, SIBM and IBS

Robert Adler; John Verzani

doi:10.1214/aop/1019160126

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Home > Journals > Ann. Probab. > Volume 28 > Issue 1 > Article

January 2000 IBM, SIBM and IBS

Robert Adler, John Verzani

Ann. Probab. 28(1): 462-477 (January 2000). DOI: 10.1214/aop/1019160126

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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.

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Robert Adler. John Verzani. "IBM, SIBM and IBS." Ann. Probab. 28 (1) 462 - 477, January 2000. https://doi.org/10.1214/aop/1019160126

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Published: January 2000

First available in Project Euclid: 18 April 2002

zbMATH: 1044.60077

MathSciNet: MR1756012

Digital Object Identifier: 10.1214/aop/1019160126

Subjects:

Primary: 60G17 , 60G57

Secondary: 60H15

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

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