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

Kouji Yano

ESAIM: Probability and Statistics (2011)

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

Abstract

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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.

How to cite

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Yano, 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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  1. A. Beck and D.P. Giesy, P-uniform convergence and a vector-valued strong law of large numbers. Trans. Amer. Math. Soc.147 (1970) 541–559.  Zbl0198.51006
  2. T. Funaki, Y. Hariya and M. Yor, Wiener integrals for centered Bessel and related processes, II. ALEA Lat. Am. J. Probab. Math. Stat.1 (2006) 225–240 (electronic).  Zbl1112.60042
  3. T. Funaki, Y. Hariya and M. Yor, Wiener integrals for centered powers of Bessel processes, I. Markov Process. Relat. Fields13 (2007) 21–56.  Zbl1123.60035
  4. T. Funaki, Y. Hariya, F. Hirsch and M. Yor, On the construction of Wiener integrals with respect to certain pseudo-Bessel processes. Stoch. Process. Appl.116 (2006) 1690–1711.  Zbl1110.60055
  5. T. Funaki, Y. Hariya, F. Hirsch and M. Yor, On some Fourier aspects of the construction of certain Wiener integrals. Stoch. Process. Appl.117 (2007) 1–22.  Zbl1113.60055
  6. P. Gosselin and T. Wurzbacher, 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.  Zbl0884.60046
  7. T. Jeulin and M. Yor, 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.  Zbl0419.60049
  8. J. Najnudel, B. Roynette and M. Yor, A remarkable σ-finite measure on 𝒞 ( ℝ + , ℝ ) related to many Brownian penalisations. C. R. Math. Acad. Sci. Paris345 (2007) 459–466.  Zbl1221.60003
  9. J. Najnudel, B. Roynette and M. Yor, A global view of Brownian penalisations. MSJ Memoirs19, Mathematical Society of Japan, Tokyo (2009).  Zbl1180.60004
  10. B. Roynette and M. Yor, Penalising Brownian paths. Lecture Notes in Math.1969, Springer, Berlin (2009).  Zbl1190.60002
  11. B. Roynette, P. Vallois and M. Yor, Some penalisations of the Wiener measure. Jpn J. Math.1 (2006) 263–290.  
  12. K. Yano, Cameron-Martin formula for the σ-finite measure unifying Brownian penalisations. J. Funct. Anal.258 (2010) 3492–3516.  Zbl1194.60049
  13. 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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