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.
Keywords: 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},
year = {2011},
publisher = {EDP Sciences},
volume = {15},
doi = {10.1051/ps/2010024},
language = {en},
url = {https://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 - https://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 https://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
[1] and , P-uniform convergence and a vector-valued strong law of large numbers. Trans. Amer. Math. Soc. 147 (1970) 541-559. | Zbl | MR
[2] , and , Wiener integrals for centered Bessel and related processes, II. ALEA Lat. Am. J. Probab. Math. Stat. 1 (2006) 225-240 (electronic). | Zbl | MR
[3] , and , Wiener integrals for centered powers of Bessel processes, I. Markov Process. Relat. Fields 13 (2007) 21-56. | Zbl | MR
[4] , , and , On the construction of Wiener integrals with respect to certain pseudo-Bessel processes. Stoch. Process. Appl. 116 (2006) 1690-1711. | Zbl | MR
[5] , , and , On some Fourier aspects of the construction of certain Wiener integrals. Stoch. Process. Appl. 117 (2007) 1-22. | Zbl | MR
[6] and , An Itô type isometry for loops in Rd via the Brownian bridge, in Séminaire de Probabilités XXXI. Lecture Notes in Math. 1655, Springer, Berlin (1997) 225-231. | Zbl | MR | Numdam
[7] and , Inégalité de Hardy, semimartingales, et faux-amis, in Séminaire de Probabilités XIII (Univ. Strasbourg, Strasbourg, 1977-1978). Lecture Notes in Math. 721, Springer, Berlin (1979) 332-359. | Zbl | MR | Numdam
[8] , and , A remarkable σ-finite measure on (, ) related to many Brownian penalisations. C. R. Math. Acad. Sci. Paris 345 (2007) 459-466. | Zbl | MR
[9] , and , A global view of Brownian penalisations. MSJ Memoirs 19, Mathematical Society of Japan, Tokyo (2009). | Zbl | MR
[10] and , Penalising Brownian paths. Lecture Notes in Math. 1969, Springer, Berlin (2009). | Zbl | MR
[11] , and , Some penalisations of the Wiener measure. Jpn J. Math. 1 (2006) 263-290. | Zbl | MR
[12] , Cameron-Martin formula for the σ-finite measure unifying Brownian penalisations. J. Funct. Anal. 258 (2010) 3492-3516. | Zbl | MR
[13] , and , Penalising symmetric stable Lévy paths. J. Math. Soc. Jpn 61 (2009) 757-798. | Zbl
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