The Annals of Probability


Robert Adler and John Verzani

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

First available in Project Euclid: 18 April 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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

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