Survival of a snake in an hostile environment
Résumé
We consider a Brownian snake subjected to killing in an inhomogeneous medium. We show an equation satisfied by the probability of survival. Conditionally on survival, the Brownian snake has the law of a snake with a drift that we specify. This study include ``path-dependent killings''. In the case of constant drift, we give a large deviation principle and derive some estimates for the caracteristics of this process. The results can also be stated in terms of super-Brownian motion and super-Brownian motion with drift. Then, we show how to annihilate a (general non-positive) drift by adding immigration. The conditioning to non-extinction of super-Brownian motion with constant non-positive drift is also studied.
Origine : Fichiers produits par l'(les) auteur(s)
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