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The Annals of Probability

Strong clumping of super-Brownian motion in a stable catalytic medium

Donald A. Dawson, Klaus Fleischmann, and Peter Mörters
Source: Ann. Probab. Volume 30, Number 4 (2002), 1990-2045.

Abstract

A typical feature of the long time behavior of continuous super-Brownian motion in a stable catalytic medium is the development of large mass clumps (or clusters) at spatially rare sites. We describe this phenomenon by means of a functional limit theorem under renormalization. The limiting process is a Poisson point field of mass clumps with no spatial motion component and with infinite variance. The mass of each cluster evolves independently according to a non-Markovian continuous process trapped at mass zero, which we describe explicitly by means of a Brownian snake construction in a random medium. We also determine the survival probability and asymptotic size of the clumps.

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Primary Subjects: 60K37, 60K35, 60J80
Secondary Subjects: 60G57, 60F05
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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.aop/1039548380
Digital Object Identifier: doi:10.1214/aop/1039548380
Mathematical Reviews number (MathSciNet): MR1944014
Zentralblatt MATH identifier: 1029.60088

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OTTAWA, ONTARIO K1S 5B6 CANADA E-MAIL: ddawson@math.carleton.ca K. FLEISCHMANN WEIERSTRASS INSTITUTE FOR APPLIED ANALy SIS AND STOCHASTICS MOHRENSTR. 39 D-10117 BERLIN GERMANY E-MAIL: fleischmann@wias-berlin.de P. MÖRTERS DEPARTMENT OF MATHEMATICAL SCIENCES UNIVERSITY OF BATH CLAVERTON DOWN BATH BA2 7AY UNITED KINGDOM E-MAIL: P.Moerters@maths.bath.ac.uk

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The Annals of Probability

The Annals of Probability