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

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  • A. Dawson, Donald
  • Feng, Shui

Abstract

Large deviation principles are established for the Fleming-Viot process with neutral mutation and with selection, and the associated equilibrium measures as the sampling rate approaches zero and when the state space is equipped with the weak topology. The path-level large deviation results improve the results of Dawson and Feng (1998, Stochastic Process. Appl. 77, 207-232) in three aspects: the state space is more natural, the initial condition is relaxed, and a large deviation principle is established for the Fleming-Viot process with selection. These improvements are achieved through a detailed study of the behaviour near the boundary of the Fleming-Viot process with finite types.

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  • 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.
    • Handle: RePEc:eee:spapps:v:92:y:2001:i:1:p:131-162
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    References listed on IDEAS

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    1. 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.
    2. 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. Schraiber, Joshua G., 2014. "A path integral formulation of the Wright–Fisher process with genic selection," Theoretical Population Biology, Elsevier, vol. 92(C), pages 30-35.
    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.
    3. F. Gamboa & A. Rouault, 2010. "Canonical Moments and Random Spectral Measures," Journal of Theoretical Probability, Springer, vol. 23(4), pages 1015-1038, December.
    4. 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).
    5. 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.

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