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The biological theory of adaptive dynamics proposes a description of the long-time evolution of an asexual population, based on the assumptions of large population, rare mutations and small mutation steps. Under these assumptions, the evolution of a quantitative dominant trait in an isolated population is described by a deterministic differential equation called 'canonical equation of adaptive dynamics'. In this work, in order to include the effect of genetic drift in this model, we consider instead...
Motivated by the development of efficient Monte Carlo methods
for PDE models in molecular dynamics,
we establish a new probabilistic interpretation of a family of divergence form
operators with discontinuous coefficients at the interface
of two open subsets of . This family of operators includes the case of the
linearized Poisson-Boltzmann equation used to
compute the electrostatic free energy of a molecule.
More precisely, we explicitly construct a Markov process whose
infinitesimal generator...
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