Wiener integral for the coordinate process is defined under the σ-finite measure unifying Brownian penalisations, which has been introduced by [Najnudel et al., C. R. Math. Acad. Sci. Paris 345 (2007) 459-466] and [Najnudel et al., MSJ Memoirs 19. Mathematical Society of Japan, Tokyo (2009)]. Its decomposition before and after last exit time from 0 is studied. This study prepares for the author's recent study [K. Yano, J. Funct. Anal. 258 (2010) 3492-3516] of Cameron-Martin formula for the σ-finite measure.
Mots-clés : stochastic integral, brownian motion, Bessel process, penalisation
@article{PS_2011__15__S69_0,
author = {Yano, Kouji},
title = {Wiener integral for the coordinate process under the $\sigma $-finite measure unifying brownian penalisations},
journal = {ESAIM: Probability and Statistics},
pages = {S69--S84},
publisher = {EDP-Sciences},
volume = {15},
year = {2011},
doi = {10.1051/ps/2010024},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ps/2010024/}
}
TY - JOUR AU - Yano, Kouji TI - Wiener integral for the coordinate process under the $\sigma $-finite measure unifying brownian penalisations JO - ESAIM: Probability and Statistics PY - 2011 SP - S69 EP - S84 VL - 15 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps/2010024/ DO - 10.1051/ps/2010024 LA - en ID - PS_2011__15__S69_0 ER -
%0 Journal Article %A Yano, Kouji %T Wiener integral for the coordinate process under the $\sigma $-finite measure unifying brownian penalisations %J ESAIM: Probability and Statistics %D 2011 %P S69-S84 %V 15 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ps/2010024/ %R 10.1051/ps/2010024 %G en %F PS_2011__15__S69_0
Yano, Kouji. Wiener integral for the coordinate process under the $\sigma $-finite measure unifying brownian penalisations. ESAIM: Probability and Statistics, Tome 15 (2011), pp. S69-S84. doi : 10.1051/ps/2010024. http://www.numdam.org/articles/10.1051/ps/2010024/
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