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10 papers · 2 filters
Stability of Feynman-Kac formulae with path-dependent potentials
Nicolas Chopin, Pierre Del Moral, Sylvain Rubenthaler
Several particle algorithms admit a Feynman-Kac representation such that the potential function may be expressed as a recursive function which depends on the complete state traject…
Total progeny in killed branching random walk
Louigi Addario-Berry, Nicolas Broutin
We consider a branching random walk for which the maximum position of a particle in the n'th generation, M_n, has zero speed on the linear scale: M_n/n --> 0 as n --> infinity. We…
A Ferguson-Klass-LePage series representation of multistable multifractional processes and related processes
Ronan Le Guével, Jacques Lévy-Véhel
The study of non-stationary processes whose local form has controlled properties is a fruitful and important area of research, both in theory and applications. We present here a co…
Global existence for rough differential equations under linear growth conditions
Massimiliano Gubinelli, Antoine Lejay
We prove existence of global solutions for differential equations driven by a geometric rough path under the condition that the vector fields have linear growth. We show by an expl…
Large deviations for singular and degenerate diffusion models in adaptive evolution
Nicolas Champagnat
In the course of Darwinian evolution of a population, punctualism is an important phenomenon whereby long periods of genetic stasis alternate with short periods of rapid evolutiona…
The continuum limit of critical random graphs
Louigi Addario-Berry, Nicolas Broutin, Christina Goldschmidt
We consider the Erdos-Renyi random graph G(n,p) inside the critical window, that is when p=1/n+ lambda*n^{-4/3}, for some fixed lambda in R. Then, as a metric space with the graph…