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On the weak convergence of Wright-Fisher model

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  • Guess, Harry A.

Abstract

We prove that the sequence of stochastic processes obtained from Wright-Fisher models by transforming the time scales and state spaces in the usual way converges weakly to a diffusion process on the time interval [0,[infinity]). Convergence of fixation probabilities and fixation time distributions are obtained as corollaries. These results extend a theorem of Watterson, who proved convergence in distribution to a diffusion at any given single time point for these processes.

Suggested Citation

  • Guess, Harry A., 1973. "On the weak convergence of Wright-Fisher model," Stochastic Processes and their Applications, Elsevier, vol. 1(3), pages 287-306, July.
    • Handle: RePEc:eee:spapps:v:1:y:1973:i:3:p:287-306
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    Cited by:

    1. Nicolas Bouleau & Christophe Chorro, 2015. "The impact of randomness on the distribution of wealth: Some economic aspects of the Wright-Fisher diffusion process," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01162452, HAL.
    2. Nicolas Bouleau & Christophe Chorro, 2015. "The impact of randomness on the distribution of wealth: Some economic aspects of the Wright-Fisher diffusion process," Documents de travail du Centre d'Economie de la Sorbonne 15024, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    3. Nicolas Bouleau & Christophe Chorro, 2015. "The impact of randomness on the distribution of wealth: Some economic aspects of the Wright-Fisher diffusion process," Post-Print halshs-01162452, HAL.
    4. Bouleau, Nicolas & Chorro, Christophe, 2017. "The impact of randomness on the distribution of wealth: Some economic aspects of the Wright–Fisher diffusion process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 479(C), pages 379-395.
    5. Nicolas Bouleau & Christophe Chorro, 2017. "The impact of randomness on the distribution of wealth: Some economic aspects of the Wright-Fisher diffusion process," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01138383, HAL.
    6. Nicolas Bouleau & Christophe Chorro, 2015. "The impact of randomness on the distribution of wealth: Some economic aspects of the Wright-Fisher diffusion process," Documents de travail du Centre d'Economie de la Sorbonne 15024r, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Jul 2015.
    7. Agostino Capponi & W. Allen Cheng & Sriram Rajan, 2015. "Systemic Risk: The Dynamics under Central Clearing," Working Papers 15-08, Office of Financial Research, US Department of the Treasury.
    8. Nicolas Bouleau & Christophe Chorro, 2017. "The impact of randomness on the distribution of wealth: Some economic aspects of the Wright-Fisher diffusion process," Post-Print hal-01138383, HAL.

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