We study some limit theorems for the normalized law of integrated Brownian motion perturbed by several examples of functionals: the first passage time, the th 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 th passage time is independent of , 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.
DOI : 10.1051/ps/2014018
Mots clés : Integrated Brownian motion, penalization, passage times
@article{PS_2015__19__148_0, author = {Profeta, Christophe}, title = {Some limiting laws associated with the integrated {Brownian} motion}, journal = {ESAIM: Probability and Statistics}, pages = {148--171}, publisher = {EDP-Sciences}, volume = {19}, year = {2015}, doi = {10.1051/ps/2014018}, mrnumber = {3386368}, zbl = {1333.60180}, language = {en}, url = {http://www.numdam.org/articles/10.1051/ps/2014018/} }
TY - JOUR AU - Profeta, Christophe TI - Some limiting laws associated with the integrated Brownian motion JO - ESAIM: Probability and Statistics PY - 2015 SP - 148 EP - 171 VL - 19 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps/2014018/ DO - 10.1051/ps/2014018 LA - en ID - PS_2015__19__148_0 ER -
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. http://www.numdam.org/articles/10.1051/ps/2014018/
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