The brownian burglar : conditioning brownian motion by its local time process
Séminaire de probabilités de Strasbourg, Tome 32 (1998), p. 328-342
@article{SPS_1998__32__328_0,
     author = {Warren, Jonathan and Yor, Marc},
     title = {The brownian burglar : conditioning brownian motion by its local time process},
     journal = {S\'eminaire de probabilit\'es de Strasbourg},
     publisher = {Springer - Lecture Notes in Mathematics},
     volume = {32},
     year = {1998},
     pages = {328-342},
     zbl = {0924.60072},
     mrnumber = {1655303},
     language = {en},
     url = {http://www.numdam.org/item/SPS_1998__32__328_0}
}
Warren, Jonathan; Yor, Marc. The brownian burglar : conditioning brownian motion by its local time process. Séminaire de probabilités de Strasbourg, Tome 32 (1998) pp. 328-342. https://www.numdam.org/item/SPS_1998__32__328_0/

[1] D. Bakry. Remarques sur les semi-groupes de Jacobi. In Hommage à P.A. Meyer et J. Neveu. Asterisque 236, pages 23-40. Soc. Math. France, 1996. | MR 1417973 | Zbl 0859.47026

[2] Ph. Biane,J.F. Le Gall , and M. Yor. Un processus qui ressemble au pont brownien. In Séminaire de Probabilités XXI, Lecture notes in Mathematics 1247, pages 270-275. Springer, 1987. | Numdam | MR 941990 | Zbl 0621.60086

[3] N. Bouleau and M. Yor. Sur la variation quadratique des temps locaux de certaines semimartingales. Comptes Rendus Acad. Sci., Paris, 292:491-494, 1981. | MR 612544 | Zbl 0476.60046

[4] I.P. Cornfeld, S.V. Fomin, and Ya.G. Sinai . Ergodic theory. Springer-Verlag, Berlin, 1982. | MR 832433 | Zbl 0493.28007

[5] D.A. Dawson. Measure-valued Markov processes. In Ecole d'Eté de Probabilitiés de Saint-Flour, 1991, Lecture Notes in Mathematics 1541. Springer, Berlin, 1993. | MR 1242575 | Zbl 0799.60080

[6] F. Delbaen and H. Shirakawa. Interest rate model with upper and lower bounds. Preprint, 1996.

[7] A. Etheridge and P. March. A note on superprocesses. Probability Theory and Related Fields, 89:141-147, 1991. | MR 1110534 | Zbl 0722.60076

[8] S.N. Ethier and T.G. Kurtz. Markov processes: characterization and convergence. Wiley, New York, 1986. | MR 838085 | Zbl 0592.60049

[9] S. Karlin and H.M. Taylor. A second course in stochastic processes. Academic Press, New York, 1981. | MR 611513 | Zbl 0469.60001

[10] M. Kimura. Diffusion models in population genetics. Journal of Applied Probability, 1:177-232, 1964. | MR 172727 | Zbl 0134.38103

[11] O. Mazet. Classification des semigroupes de diffusion sur R associés à une famille de polynomes orthogonaux. In Séminaire de Probabilités XXXI, Lecture notes in Mathematics 1655, pages 40-53. Springer, Berlin, 1997. | Numdam | MR 1478714 | Zbl 0883.60072

[12] K.R. Parthasarathy. Introduction to probability and measure. Macmillan, London, 1977. | Zbl 0395.28001

[13] J. Pitman and M. Yor. Sur une décomposition des ponts de Bessel. In Functional analysis in Markov processes, Lecture notes in Mathematics 923, pages 276-285. Springer, Berlin, 1982. | MR 661630 | Zbl 0499.60082

[14] J. Pitman and M. Yor. Decomposition at the maximum for excursions and bridges of one-dimensional diffusions. In M. Fukushima, N. Ikeda, H. Kunita, and S. Watanabe, editors, Itô's stochastic calculus and probability theory, pages 293-310. Springer, 1996. | MR 1439532 | Zbl 0877.60053

[15] D. Revuz and M. Yor. Continuous martingales and Brownian motion. Springer, Berlin, 1991. | MR 1083357 | Zbl 0731.60002

[16] V.A. Rohlin. Selected topics in the metric theory of dynamical systems. American Mathematical Society Translations Series 2, 49:171-240, 1966. | Zbl 0185.21802

[17] A. Vershik and M. Yor. Multiplicativité du processus gamma et étude asymptotique des lois stables d'indice α, lorsque α tend vers 0. Technical Report 289, Laboratoire de Probabilités, Université Pierre et Marie Curie, Paris, 1995.

[18] J. Warren and M. Yor. Skew-products involving Bessel and Jacobi processes. Technical report, Statistics group, University of Bath, 1997.