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

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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Cited literature [10 references]

https://hal.archives-ouvertes.fr/hal-00257593
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Submitted on : Tuesday, February 19, 2008 - 5:09:51 PM
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• HAL Id : hal-00257593, version 1

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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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