Penalization of the Wiener measure and principal values
Catherine Donati-Martin; Yueyun Hu
Séminaire de probabilités de Strasbourg (2002)
- Volume: 36, page 251-269
Access Full Article
topHow to cite
topDonati-Martin, Catherine, and Hu, Yueyun. "Penalization of the Wiener measure and principal values." Séminaire de probabilités de Strasbourg 36 (2002): 251-269. <http://eudml.org/doc/114091>.
@article{Donati2002,
author = {Donati-Martin, Catherine, Hu, Yueyun},
journal = {Séminaire de probabilités de Strasbourg},
keywords = {Brownian motion; Bessel process; Girsanov theorem; Krein correspondence; convergence in law of processes; diffusion},
language = {eng},
pages = {251-269},
publisher = {Springer - Lecture Notes in Mathematics},
title = {Penalization of the Wiener measure and principal values},
url = {http://eudml.org/doc/114091},
volume = {36},
year = {2002},
}
TY - JOUR
AU - Donati-Martin, Catherine
AU - Hu, Yueyun
TI - Penalization of the Wiener measure and principal values
JO - Séminaire de probabilités de Strasbourg
PY - 2002
PB - Springer - Lecture Notes in Mathematics
VL - 36
SP - 251
EP - 269
LA - eng
KW - Brownian motion; Bessel process; Girsanov theorem; Krein correspondence; convergence in law of processes; diffusion
UR - http://eudml.org/doc/114091
ER -
References
top- [1] Bertoin, J.: Applications de la théorie spectrale des cordes vibrantes aux fonctionnelles additives principales d'un brownien réfléchi. Ann. Inst. H. Poincaré Probab. Statist.25 (1989) 307-323. Zbl0694.60070MR1023954
- [2] Biane, Ph. and Yor, M.Valeurs principales associées aux temps locaux browniens. Bull. Sci. Math.111 (1987) 23-101. Zbl0619.60072MR886959
- [3] Durrett, R.T. and Rogers, L.C.G.: Asymptotic behavior of Brownian polymers. Prob. Th. Rel. Fields92 (1992) 337-349. Zbl0767.60080MR1165516
- [4] Dym, H. and McKean, H.P.: Gaussian Processes, Function Theory and the Inverse Spectral Problem. Academic Press, New York, London. 1976. Zbl0327.60029
- [5] van der Hofstad, R., den Hollander, F. and König, W.: Central limit theorem for the Edwards model. Ann. Probab.25 (1997) 573-597. Zbl0873.60009MR1434119
- [6] Imhof, J.P.: Density factorizations for Brownian motion and the three dimensional Bessel processes and applications. J. Appl. Probab.21 (1984) 500-510. Zbl0547.60081MR752015
- [7] Karatzas, I. and Shreve, S.E.: Brownian Motion and Stochastic Calculus (2nd edition) Springer, Berlin, 1991. Zbl0734.60060MR1121940
- [8] Kasahara, Y.: Spectral theory of generalized second order differential operators and its applications to Markov processes. Japan J. Math.1 (1975) 67-84. Zbl0348.60113MR405615
- [9] Kasahara, Y., Kotani, S. and Watanabe, H.: On the Green functions of 1-dimensional diffusion processes. Publ. Res. Inst. Math. Sci.16 (1980) no. 1, 175-188. Zbl0442.60077MR574032
- [10] Kotani, S. and Watanabe, S.: Krein's spectral theory of strings and generalized diffusion processes. In: "Functional Analysis in Markov Processes" (Ed. M. Fukushima) Lect. Note Math.923 (1982) pp. 235-259. SpringerBerlin. Zbl0496.60080MR661628
- [11] Krein, M.G.: On a generalization of an investigation of Stieltjes. Dokl. Akad. Nauk SSSR87 (1952) 881-884. Zbl0049.34702MR54078
- [12] Pitman, J. and Yor, M.: Bessel processes and infinitely divisible laws. In: Stochastic integrals (Proc. Sympos., Univ. Durham, Durham, 1980), pp. 285-370, Lecture Notes in Math., 851, Springer, Berlin, 1981. Zbl0469.60076MR620995
- [13] Revuz, D. and Yor, M.Continuous Martingales and Brownian Motion2nd edition, Springer, Berlin, 1994. Zbl0804.60001MR1303781
- [14] Rogers, L.C.G.and Williams, D.: Diffusions, Markov Processes and Martingales. Vol. II: Itô Calculus. Wiley, Chichester, 1987. Zbl0627.60001MR921238
- [15] Ruiz de Chavez, J.Le théorème de Paul Lévy pour des mesures signées. Sém. de Probabilités XVIII. Lecture Notes in Math.1059, 245-255, Springer, Berlin, 1984. Zbl0537.60039MR770965
- [16] Stroock, D.W. and Varadhan, S.R.S.: Multidimensional Diffusion ProcessesSpringer, Berlin, 1979. Zbl0426.60069MR532498
- [17] Watanabe, S.: Generalized arc-sine laws for one-dimensional diffusion processes and random walks. Proceedings of Symposia in Pure Mathematics (In: "Stochastic Analysis" (eds: M.C. Cranston and M.A. Pinsky)) 57157-172Providence, Rhode Island, 1995. Zbl0824.60080MR1335470
- [18] Watanabe, S.: Bilateral Bessel diffusion processes with drift and time inversion. (1999) Preprint
- [19] Yor, M.: Some Aspects of Brownian Motion. Part II: Some Recent Martingale Problems. Birkhäuser Verlag, Berlin, 1997. Zbl0880.60082MR1442263
- [20] Yor, M. (editor): Exponential Functionals and Principal Values Related to Brownian Motion (A collection of research papers).Biblioteca de la Revista Matemática Iberoamericana, Madrid1997. Zbl0889.00015MR1648653
- [21] Zvonkin, A.K.: A transformation of the phase space of a process that removes the drift. Math. USSR Sbornik2 (1974) 129-149. Zbl0306.60049MR336813
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.