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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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 $d \geqslant \alpha$.
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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