Université Paris 6Pierre et Marie Curie Université Paris 7Denis Diderot CNRS U.M.R. 7599 Probabilités et Modèles Aléatoires''

### Strict positivity of a solution to a one-dimensional Kac equation without cutoff

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Résumé: We consider the solution of a one-dimensional Kac equation without cutoff built by Graham and M\'el\'eard in \cite{gm}. Recalling that this solution is the density of a Poisson driven nonlinear stochastic differential equation, we developp Bismut's approach of the Malliavin Calculus for Poisson functionals, in order to prove that this solution is strictly positive on $]0,\infty[ \times \reel$.