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A zero-one law of almost sure local extinction for (1+[beta])-super-Brownian motion

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  • Zhou, Xiaowen

Abstract

This paper considers the following generalized almost sure local extinction for the d-dimensional (1+[beta])-super-Brownian motion X starting from Lebesgue measure on . For any t>=0 write for a closed ball in with center at 0 and radius g(t), where g is a nonnegative, nondecreasing and right continuous function on [0,[infinity]). Let For , it is shown that is equal to either 0 or 1 depending on whether the value of the integral is finite or infinite, respectively. An asymptotic upper bound for is found when .

Suggested Citation

  • Zhou, Xiaowen, 2008. "A zero-one law of almost sure local extinction for (1+[beta])-super-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 118(11), pages 1982-1996, November.
    • Handle: RePEc:eee:spapps:v:118:y:2008:i:11:p:1982-1996
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    References listed on IDEAS

    as
    1. Dawson, Donald A. & Hochberg, Kenneth J. & Vinogradov, Vladimir, 1996. "High-density limits of hierarchically structured branching-diffusing populations," Stochastic Processes and their Applications, Elsevier, vol. 62(2), pages 191-222, July.
    2. Dawson, Donald A. & Fleischmann, Klaus, 1988. "Strong clumping of critical space-time branching models in subcritical dimensions," Stochastic Processes and their Applications, Elsevier, vol. 30(2), pages 193-208, December.
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