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Comparing Fleming-Viot and Dawson-Watanabe processes

Author

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  • Ethier, S. N.
  • Krone, Stephen M.

Abstract

Fleming-Viot processes and Dawson-Watanabe processes are two classes of "superprocesses" that have received a great deal of attention in recent years. These processes have many properties in common. In this paper, we prove a result that helps to explain why this is so. It allows one to prove certain theorems for one class when they are true for the other. More specifically, we show that product moments of a Fleming-Viot process can be bounded above by the corresponding moments of the Dawson-Watanabe process with the same "underlying particle motion", and vice versa except for a multiplicative constant. As an application, we establish existence and continuity properties of local time for certain Fleming-Viot processes.

Suggested Citation

  • Ethier, S. N. & Krone, Stephen M., 1995. "Comparing Fleming-Viot and Dawson-Watanabe processes," Stochastic Processes and their Applications, Elsevier, vol. 60(2), pages 171-190, December.
    • Handle: RePEc:eee:spapps:v:60:y:1995:i:2:p:171-190
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    References listed on IDEAS

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    1. Dawson, D. A., 1975. "Stochastic evolution equations and related measure processes," Journal of Multivariate Analysis, Elsevier, vol. 5(1), pages 1-52, March.
    2. Adler, Robert J. & Lewin, Marica, 1992. "Local time and Tanaka formulae for super Brownian and super stable processes," Stochastic Processes and their Applications, Elsevier, vol. 41(1), pages 45-67, May.
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    Cited by:

    1. Dawson, D.A. & Vaillancourt, J. & Wang, H., 2021. "Joint Hölder continuity of local time for a class of interacting branching measure-valued diffusions," Stochastic Processes and their Applications, Elsevier, vol. 138(C), pages 212-233.
    2. Möhle, M., 2001. "Forward and backward diffusion approximations for haploid exchangeable population models," Stochastic Processes and their Applications, Elsevier, vol. 95(1), pages 133-149, September.
    3. da Silva, Telles Timóteo & Fragoso, Marcelo Dutra, 2012. "Absolutely continuous measure for a jump-type Fleming–Viot process," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 557-564.

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