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Large deviations for the Fleming-Viot process with neutral mutation and selection

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  • Dawson, Donald A.
  • Feng, Shui

Abstract

Large deviation principles are established for the Fleming-Viot processes with neutral mutation and selection, and the corresponding equilibrium measures as the sampling rate goes to 0. All results are first proved for the finite allele model, and then generalized, through the projective limit technique, to the infinite allele model. Explicit expressions are obtained for the rate functions.

Suggested Citation

  • Dawson, Donald A. & Feng, Shui, 1998. "Large deviations for the Fleming-Viot process with neutral mutation and selection," Stochastic Processes and their Applications, Elsevier, vol. 77(2), pages 207-232, September.
    • Handle: RePEc:eee:spapps:v:77:y:1998:i:2:p:207-232
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    References listed on IDEAS

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    1. Ethier, S. N. & Kurtz, Thomas G., 1994. "Convergence to Fleming-Viot processes in the weak atomic topology," Stochastic Processes and their Applications, Elsevier, vol. 54(1), pages 1-27, November.
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    Cited by:

    1. 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.
    2. Gao, Fuqing & Gao, Yunshi & Xiong, Jie, 2024. "Fluctuations and moderate deviations for a catalytic Fleming–Viot branching system in nonequilibrium," Stochastic Processes and their Applications, Elsevier, vol. 171(C).
    3. Fatheddin, Parisa & Xiong, Jie, 2015. "Large deviation principle for some measure-valued processes," Stochastic Processes and their Applications, Elsevier, vol. 125(3), pages 970-993.
    4. A. Dawson, Donald & Feng, Shui, 2001. "Large deviations for the Fleming-Viot process with neutral mutation and selection, II," Stochastic Processes and their Applications, Elsevier, vol. 92(1), pages 131-162, March.

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