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Published online by Cambridge University Press: 14 July 2016
Let Xt be a Feller (branching) diffusion with drift αx. We consider new processes, the probability measures of which are obtained from that of X via changes of measure involving suitably normalized exponential functions of with λ > 0. The new processes can be thought of as ‘self-reinforcing’ versions of the old.
Depending on the values of α, T and λ, the process under the new measure is shown to exhibit explosion in finite time. We also obtain a number of other results related to the new processes.
Since the Feller diffusion is also the total mass process of a superprocess, we relate the finite-time explosion property to the behaviour of superprocesses with local self-interaction, and raise some interesting questions for these.
Research supported in part by US–Israel Binational Science Foundation, Israel Science Foundation, and National Science Foundation (RJA).
Research supported in part by ONR Grant No. N00014-94-1-0191 (SKI).