Survival of a snake in an hostile environment

Laurent Serlet (1)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal

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.

Mots clés: Super-Brownian motion; Killing in an inhomogeneous medium; Brownian snake; Conditioning to non-extinction

Domaines: Probabilités [math.PR]

Laurent Serlet. Survival of a snake in an hostile environment. 2007. ⟨hal-00473921⟩