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 $d = \alpha$.
Publié le : 1979-08-14
Classification:
Random measure,
measure diffusion process,
Hausdorff dimension,
60J80,
60J60,
55C10
@article{1176994991,
author = {Dawson, Donald A. and Hochberg, Kenneth J.},
title = {The Carrying Dimension of a Stochastic Measure Diffusion},
journal = {Ann. Probab.},
volume = {7},
number = {6},
year = {1979},
pages = { 693-703},
language = {en},
url = {http://dml.mathdoc.fr/item/1176994991}
}
Dawson, Donald A.; Hochberg, Kenneth J. The Carrying Dimension of a Stochastic Measure Diffusion. Ann. Probab., Tome 7 (1979) no. 6, pp. 693-703. http://gdmltest.u-ga.fr/item/1176994991/