## A space-time property of a class of measure-valued branching diffusions

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- by Edwin A. Perkins PDF
- Trans. Amer. Math. Soc.
**305**(1988), 743-795 Request permission

## Abstract:

If $d > \alpha$, it is shown that the $d$-dimensional branching diffusion of index $\alpha$, studied by Dawson and others, distributes its mass over a random support in a uniform manner with respect to the Hausdorff ${\phi _\alpha }$-measure, where ${\phi _\alpha }(x) = {x^\alpha }\log \log 1/x$. More surprisingly, it does so for all positive times simultaneously. Slightly less precise results are obtained in the critical case $d = \alpha$. In particular, the process is singular at all positive times a.s. for $d \geqslant \alpha$.## References

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## Additional Information

- © Copyright 1988 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**305**(1988), 743-795 - MSC: Primary 60G57; Secondary 60J60, 60J80
- DOI: https://doi.org/10.1090/S0002-9947-1988-0924777-0
- MathSciNet review: 924777