# Wiener integral for the coordinate process under the σ-finite measure unifying Brownian penalisations

ESAIM: Probability and Statistics (2011)

- Volume: 15, page S69-S84
- ISSN: 1292-8100

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topYano, Kouji. "Wiener integral for the coordinate process under the σ-finite measure unifying Brownian penalisations." ESAIM: Probability and Statistics 15 (2011): S69-S84. <http://eudml.org/doc/197740>.

@article{Yano2011,

abstract = {
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. Paris345 (2007) 459–466] and [Najnudel et al., MSJ Memoirs19. 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.
},

author = {Yano, Kouji},

journal = {ESAIM: Probability and Statistics},

keywords = {Stochastic integral; Brownian motion;
Bessel process; penalisation},

language = {eng},

month = {5},

pages = {S69-S84},

publisher = {EDP Sciences},

title = {Wiener integral for the coordinate process under the σ-finite measure unifying Brownian penalisations},

url = {http://eudml.org/doc/197740},

volume = {15},

year = {2011},

}

TY - JOUR

AU - Yano, Kouji

TI - Wiener integral for the coordinate process under the σ-finite measure unifying Brownian penalisations

JO - ESAIM: Probability and Statistics

DA - 2011/5//

PB - EDP Sciences

VL - 15

SP - S69

EP - S84

AB -
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. Paris345 (2007) 459–466] and [Najnudel et al., MSJ Memoirs19. 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.

LA - eng

KW - Stochastic integral; Brownian motion;
Bessel process; penalisation

UR - http://eudml.org/doc/197740

ER -

## References

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- J. Najnudel, B. Roynette and M. Yor, A remarkable σ-finite measure on $\mathcal{C}$(${\mathbb{R}}_{+}$, $\mathbb{R}$) related to many Brownian penalisations. C. R. Math. Acad. Sci. Paris345 (2007) 459–466. Zbl1221.60003
- J. Najnudel, B. Roynette and M. Yor, A global view of Brownian penalisations. MSJ Memoirs19, Mathematical Society of Japan, Tokyo (2009). Zbl1180.60004
- B. Roynette and M. Yor, Penalising Brownian paths. Lecture Notes in Math.1969, Springer, Berlin (2009). Zbl1190.60002
- B. Roynette, P. Vallois and M. Yor, Some penalisations of the Wiener measure. Jpn J. Math.1 (2006) 263–290.
- K. Yano, Cameron-Martin formula for the σ-finite measure unifying Brownian penalisations. J. Funct. Anal.258 (2010) 3492–3516. Zbl1194.60049
- K. Yano, Y. Yano and M. Yor, Penalising symmetric stable Lévy paths. J. Math. Soc. Jpn61 (2009) 757–798. Zbl1180.60008

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