Local limit theorems for Brownian additive functionals and penalisation of Brownian paths, IX

Bernard Roynette 1, 2 Marc Yor 3
2 TOSCA
INRIA Lorraine, CRISAM - Inria Sophia Antipolis - Méditerranée , UHP - Université Henri Poincaré - Nancy 1, Université Nancy 2, INPL - Institut National Polytechnique de Lorraine, CNRS - Centre National de la Recherche Scientifique : UMR7502
Abstract : We obtain a local limit theorem for the laws of a class of Brownian additive functionals and we apply this result to a penalisation problem. We study precisely the case of the additive functional : $\Big(A_t^{-} := \int_0^t 1_{X_s < 0}ds, t\geq 0\Big) $. On the other hand, we describe Feynman-Kac type penalisation results for long Brownian bridges thus completing some similar previous study for standard Brownian motion (see [RVY,I]).
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Bernard Roynette, Marc Yor. Local limit theorems for Brownian additive functionals and penalisation of Brownian paths, IX. 2008. ⟨hal-00257593⟩

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