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Absolutely continuous measure for a jump-type Fleming–Viot process

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  • da Silva, Telles Timóteo
  • Fragoso, Marcelo Dutra

Abstract

In this paper, we prove that the random measure of the one-dimensional jump-type Fleming–Viot process is absolutely continuous with respect to the Lebesgue measure in R, provided the mutation operator satisfies certain regularity conditions. This result is an important step towards the representation of the Fleming–Viot process with jumps in terms of the solution of a stochastic partial differential equation.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:3:p:557-564
    DOI: 10.1016/j.spl.2011.11.024
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    References listed on IDEAS

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    1. 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.
    2. da Silva, Telles Timóteo & Fragoso, Marcelo D., 2008. "Sample paths of jump-type Fleming-Viot processes with bounded mutation operators," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1784-1791, September.
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