Geodesic
Some limiting laws associated with the integrated Brownian motion
Profeta, Christophe1 
1 Laboratoire de Mathématiques et Modélisation d’Evry (LaMME), Université d’Evry-Val-d’Essonne, UMR CNRS 8071, 91037 Evry cedex, France.
ESAIM: Probability and Statistics, Tome 19 (2015), pp. 148-171

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We study some limit theorems for the normalized law of integrated Brownian motion perturbed by several examples of functionals: the first passage time, the nth passage time, the last passage time up to a finite horizon and the supremum. We show that the penalization principle holds in all these cases and give descriptions of the conditioned processes. In particular, it is remarkable that the penalization by the nth passage time is independent of n, and always gives the same penalized process, i.e. integrated Brownian motion conditioned not to hit 0. Our results rely on some explicit formulae obtained by Lachal and on enlargement of filtrations.

Reçu le :
DOI : 10.1051/ps/2014018
Classification : 60J65, 60G15, 60G44
Keywords: Integrated Brownian motion, penalization, passage times

Profeta, Christophe 1

1 Laboratoire de Mathématiques et Modélisation d’Evry (LaMME), Université d’Evry-Val-d’Essonne, UMR CNRS 8071, 91037 Evry cedex, France. 
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     author = {Profeta, Christophe},
     title = {Some limiting laws associated with the integrated {Brownian} motion},
     journal = {ESAIM: Probability and Statistics},
     pages = {148--171},
     publisher = {EDP-Sciences},
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     year = {2015},
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Profeta, Christophe. Some limiting laws associated with the integrated Brownian motion. ESAIM: Probability and Statistics, Tome 19 (2015), pp. 148-171. doi: 10.1051/ps/2014018

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