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August, 1979 The Carrying Dimension of a Stochastic Measure Diffusion
Donald A. Dawson, Kenneth J. Hochberg
Ann. Probab. 7(4): 693-703 (August, 1979). DOI: 10.1214/aop/1176994991


A multiplicative stochastic measure diffusion process in $R^d$ is the continuous analogue of an infinite particle branching Markov process in which the particles move in $R^d$ according to a symmetric stable process of index $\alpha 0 < \alpha \leqslant 2$. The main result of this paper is that there is a random carrying set whose Hausdorff dimension is almost surely less than or equal to $\alpha$. As a corollary it follows that the corresponding random measure is singular for $d > \alpha$. The latter result is also proved by a different approach in the case $d = \alpha$.


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Donald A. Dawson. Kenneth J. Hochberg. "The Carrying Dimension of a Stochastic Measure Diffusion." Ann. Probab. 7 (4) 693 - 703, August, 1979.


Published: August, 1979
First available in Project Euclid: 19 April 2007

zbMATH: 0411.60084
MathSciNet: MR537215
Digital Object Identifier: 10.1214/aop/1176994991

Primary: 60J80
Secondary: 55C10 , 60J60

Keywords: Hausdorff dimension , measure diffusion process , random measure

Rights: Copyright © 1979 Institute of Mathematical Statistics


Vol.7 • No. 4 • August, 1979
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