Convergence of an infinite dimensional stochastic process to a spatially structured trait substitution sequence

  title={Convergence of an infinite dimensional stochastic process to a spatially structured trait substitution sequence},
  author={H{\'e}l{\`e}ne Leman},
  journal={Stochastics and Partial Differential Equations: Analysis and Computations},
  • H. Leman
  • Published 7 September 2015
  • Mathematics
  • Stochastics and Partial Differential Equations: Analysis and Computations
We consider an individual-based spatially structured population for Darwinian evolution in an asexual population. The individuals move randomly on a bounded continuous space according to a reflected brownian motion. The dynamics involves also a birth rate, a density-dependent logistic death rate and a probability of mutation at each birth event. We study the convergence of the microscopic process in a long time scale when the population size grows to $$+\infty $$+∞ and the mutation probability… 
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