Displaying similar documents to “Exponential functionals of Brownian motion. I: Probability laws at fixed time.”

Penalisations of multidimensional Brownian motion, VI

Bernard Roynette, Pierre Vallois, Marc Yor (2009)

ESAIM: Probability and Statistics

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As in preceding papers in which we studied the limits of penalized 1-dimensional Wiener measures with certain functionals Γ, we obtain here the existence of the limit, as → ∞, of -dimensional Wiener measures penalized by a function of the maximum up to time of the Brownian winding process (for ), or in 2 dimensions for Brownian motion prevented to exit a cone before time . Various extensions of these multidimensional penalisations are studied, and the limit laws...

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

Bernard Roynette, Marc Yor (2010)

ESAIM: Probability and Statistics

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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: ( A t - : = ∫ 0 t 1 X s < 0 d s , t ≥ 0 ) . 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 [B. Roynette, P. Vallois and M. Yor, (2006) 171–246]).