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

@article{Leman2015ConvergenceOA, 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}, year={2015}, volume={4}, pages={791-826} }

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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