Penalization of the Wiener measure and principal values
Séminaire de probabilités de Strasbourg, Volume 36  (2002), p. 251-269
@article{SPS_2002__36__251_0,
     author = {Donati-Martin, Catherine and Hu, Yueyun},
     title = {Penalization of the Wiener measure and principal values},
     journal = {S\'eminaire de probabilit\'es de Strasbourg},
     publisher = {Springer - Lecture Notes in Mathematics},
     volume = {36},
     year = {2002},
     pages = {251-269},
     zbl = {1047.60076},
     mrnumber = {1971590},
     language = {en},
     url = {http://www.numdam.org/item/SPS_2002__36__251_0}
}
Donati-Martin, Catherine; Hu, Yueyun. Penalization of the Wiener measure and principal values. Séminaire de probabilités de Strasbourg, Volume 36 (2002) , pp. 251-269. http://www.numdam.org/item/SPS_2002__36__251_0/

[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. | Numdam | MR 1023954 | Zbl 0694.60070

[2] Biane, Ph. and Yor, M. Valeurs principales associées aux temps locaux browniens. Bull. Sci. Math. 111 (1987) 23-101. | MR 886959 | Zbl 0619.60072

[3] Durrett, R.T. and Rogers, L.C.G.: Asymptotic behavior of Brownian polymers. Prob. Th. Rel. Fields 92 (1992) 337-349. | MR 1165516 | Zbl 0767.60080

[4] Dym, H. and Mckean, H.P.: Gaussian Processes, Function Theory and the Inverse Spectral Problem. Academic Press, New York, London. 1976. | Zbl 0327.60029

[5] Van Der Hofstad, R., Den Hollander, F. and König, W.: Central limit theorem for the Edwards model. Ann. Probab. 25 (1997) 573-597. | MR 1434119 | Zbl 0873.60009

[6] Imhof, J.P.: Density factorizations for Brownian motion and the three dimensional Bessel processes and applications. J. Appl. Probab. 21 (1984) 500-510. | MR 752015 | Zbl 0547.60081

[7] Karatzas, I. and Shreve, S.E.: Brownian Motion and Stochastic Calculus (2nd edition) Springer, Berlin, 1991. | MR 1121940 | Zbl 0734.60060

[8] Kasahara, Y.: Spectral theory of generalized second order differential operators and its applications to Markov processes. Japan J. Math. 1 (1975) 67-84. | MR 405615 | Zbl 0348.60113

[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. | MR 574032 | Zbl 0442.60077

[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. Springer Berlin. | MR 661628 | Zbl 0496.60080

[11] Krein, M.G.: On a generalization of an investigation of Stieltjes. Dokl. Akad. Nauk SSSR 87 (1952) 881-884. | MR 54078 | Zbl 0049.34702

[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. | MR 620995 | Zbl 0469.60076

[13] Revuz, D. and Yor, M. Continuous Martingales and Brownian Motion 2nd edition, Springer, Berlin, 1994. | MR 1303781 | Zbl 0804.60001

[14] Rogers, L.C.G. and Williams, D.: Diffusions, Markov Processes and Martingales. Vol. II: Itô Calculus. Wiley, Chichester, 1987. | MR 921238 | Zbl 0627.60001

[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. | Numdam | MR 770965 | Zbl 0537.60039

[16] Stroock, D.W. and Varadhan, S.R.S.: Multidimensional Diffusion Processes Springer, Berlin, 1979. | MR 532498 | Zbl 0426.60069

[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)) 57157-172 Providence, Rhode Island, 1995. | MR 1335470 | Zbl 0824.60080

[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. | MR 1442263 | Zbl 0880.60082

[20] Yor, M. (editor): Exponential Functionals and Principal Values Related to Brownian Motion (A collection of research papers). Biblioteca de la Revista Matemática Iberoamericana, Madrid 1997. | MR 1648653 | Zbl 0889.00015

[21] Zvonkin, A.K.: A transformation of the phase space of a process that removes the drift. Math. USSR Sbornik 2 (1974) 129-149. | MR 336813 | Zbl 0306.60049