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High-density limits of hierarchically structured branching-diffusing populations

Author

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  • Dawson, Donald A.
  • Hochberg, Kenneth J.
  • Vinogradov, Vladimir

Abstract

We develop a general probabilistic approach that enables one to get sharp estimates for the almost-sure short-term behavior of hierarchically structured branching-diffusion processes. This approach involves the thorough investigation of the cluster structure and the derivation of some probability estimates for the sets of rapidly fluctuating realizations. In addition, our approach leads to the derivation of new modulus-of-continuity-type results for measure-valued processes. In turn, the modulus-of-continuity-type results for hierarchical branching-diffusion processes are used to derive upper estimates for the Hausdorff dimension of support.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:62:y:1996:i:2:p:191-222
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    References listed on IDEAS

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    1. Bojdecki, Tomasz & Gorostiza, Luis G., 1995. "Self-intersection local time for Gaussian '(d)-processes: Existence, path continuity and examples," Stochastic Processes and their Applications, Elsevier, vol. 60(2), pages 191-226, December.
    2. El Karoui, Nicole & Roelly, Sylvie, 1991. "Propriétés de martingales, explosion et représentation de Lévy--Khintchine d'une classe de processus de branchement à valeurs mesures," Stochastic Processes and their Applications, Elsevier, vol. 38(2), pages 239-266, August.
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    Cited by:

    1. 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.
    2. D. A. Dawson & L. G. Gorostiza & A. Wakolbinger, 2001. "Occupation Time Fluctuations in Branching Systems," Journal of Theoretical Probability, Springer, vol. 14(3), pages 729-796, July.

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