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An example and a conjecture concerning scaling limits of superdiffusions

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  • Engländer, János

Abstract

Consider the superdiffusion corresponding to the semilinear operator Lu+[beta]u-[alpha]u2 on . In [Engländer and Turaev, 2002], the existence of the random measurewas shown under appropriate spectral theoretical assumptions. In the same paper we asked whether the probability of having a zero limit is the same as the probability of finite time extinction. In this note we give an answer in the negative by showing a counterexample.

Suggested Citation

  • Engländer, János, 2004. "An example and a conjecture concerning scaling limits of superdiffusions," Statistics & Probability Letters, Elsevier, vol. 66(3), pages 363-368, February.
    • Handle: RePEc:eee:stapro:v:66:y:2004:i:3:p:363-368
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    References listed on IDEAS

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    1. Fleischmann, Klaus & Swart, Jan M., 2003. "Extinction versus exponential growth in a supercritical super-Wright-Fisher diffusion," Stochastic Processes and their Applications, Elsevier, vol. 106(1), pages 141-165, July.
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