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2019 Scaling limits of population and evolution processes in random environment
Vincent Bansaye, Maria-Emilia Caballero, Sylvie Méléard
Electron. J. Probab. 24: 1-38 (2019). DOI: 10.1214/19-EJP262


We propose a general method for investigating scaling limits of finite dimensional Markov chains to diffusions with jumps. The results of tightness, identification and convergence in law are based on the convergence of suitable characteristics of the chain transition. We apply these results to population processes recursively defined as sums of independent random variables. Two main applications are developed. First, we extend the Wright-Fisher model to independent and identically distributed random environments and show its convergence, under a large population assumption, to a Wright-Fisher diffusion in random environment. Second, we obtain the convergence in law of generalized Galton-Watson processes with interaction in random environment to solutions of stochastic differential equations with jumps.


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Vincent Bansaye. Maria-Emilia Caballero. Sylvie Méléard. "Scaling limits of population and evolution processes in random environment." Electron. J. Probab. 24 1 - 38, 2019.


Received: 19 February 2018; Accepted: 2 January 2019; Published: 2019
First available in Project Euclid: 8 March 2019

zbMATH: 07055657
MathSciNet: MR3925459
Digital Object Identifier: 10.1214/19-EJP262

Primary: 60F05 , 60F10 , 60F15 , 60J27 , 60J75 , 92D25

Keywords: characteristics , Diffusions with jumps , Galton-Watson process , random environment , Semimartingales , tightness , Wright-Fisher process


Vol.24 • 2019
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