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

Published online by Cambridge University Press:  15 October 2010

Kouji Yano
Kouji Yano*
Affiliation:
Department of Mathematics, Graduate School of Science, Kobe University, Kobe, Japan. kyano@math.kobe-u.ac.jp
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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.

Keywords

Stochastic integralBrownian motionBessel processpenalisation
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 15: Supplement: In honor of Marc Yor , 2011 , pp. S69 - S84
Copyright
© EDP Sciences, SMAI, 2011

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References

Beck, A. and Giesy, D.P., P-uniform convergence and a vector-valued strong law of large numbers. Trans. Amer. Math. Soc. 147 (1970) 541–559.
Funaki, T., Hariya, Y. and Yor, M., Wiener integrals for centered Bessel and related processes, II. ALEA Lat. Am. J. Probab. Math. Stat. 1 (2006) 225–240 (electronic).
Funaki, T., Hariya, Y. and Yor, M., Wiener integrals for centered powers of Bessel processes, I. Markov Process. Relat. Fields 13 (2007) 21–56.
Funaki, T., Hariya, Y., Hirsch, F. and Yor, M., On the construction of Wiener integrals with respect to certain pseudo-Bessel processes. Stoch. Process. Appl. 116 (2006) 1690–1711. CrossRef
Funaki, T., Hariya, Y., Hirsch, F. and Yor, M., On some Fourier aspects of the construction of certain Wiener integrals. Stoch. Process. Appl. 117 (2007) 1–22. CrossRef
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.
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.
Najnudel, J., Roynette, B. and Yor, M., A remarkable σ-finite measure on $\mathcal{C}$($\mathbb{R}_+$, $\mathbb{R}$) related to many Brownian penalisations. C. R. Math. Acad. Sci. Paris 345 (2007) 459–466. CrossRef
J. Najnudel, B. Roynette and M. Yor, A global view of Brownian penalisations. MSJ Memoirs 19, Mathematical Society of Japan, Tokyo (2009).
B. Roynette and M. Yor, Penalising Brownian paths. Lecture Notes in Math. 1969, Springer, Berlin (2009).
Roynette, B., Vallois, P. and Yor, M., Some penalisations of the Wiener measure. Jpn J. Math. 1 (2006) 263–290. CrossRef
Yano, K., Cameron-Martin formula for the σ-finite measure unifying Brownian penalisations. J. Funct. Anal. 258 (2010) 3492–3516. CrossRef
Yano, K., Yano, Y. and Yor, M., Penalising symmetric stable Lévy paths. J. Math. Soc. Jpn 61 (2009) 757–798. CrossRef