IBM, SIBM and IBS. (English) Zbl 1044.60077

Summary: 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.


60J65 Brownian motion
60G17 Sample path properties
60G57 Random measures
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
Full Text: DOI


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