How long does it take a transient Bessel process to reach its future infimum?
Shi, Zhan
Séminaire de probabilités de Strasbourg, Tome 30 (1996), p. 207-217 / Harvested from Numdam
Publié le : 1996-01-01
@article{SPS_1996__30__207_0,
     author = {Shi, Zhan},
     title = {How long does it take a transient Bessel process to reach its future infimum?},
     journal = {S\'eminaire de probabilit\'es de Strasbourg},
     volume = {30},
     year = {1996},
     pages = {207-217},
     mrnumber = {1459484},
     zbl = {0857.60024},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/SPS_1996__30__207_0}
}
Shi, Zhan. How long does it take a transient Bessel process to reach its future infimum?. Séminaire de probabilités de Strasbourg, Tome 30 (1996) pp. 207-217. http://gdmltest.u-ga.fr/item/SPS_1996__30__207_0/

[B] Bertoin, J. (1991). Sur la décomposition de la trajectoire d'un processus de Lévy spectralement positif en son minimum. Ann. Inst. H. Poincaré Probab. Statist. 27 537-547. | Numdam | MR 1141246 | Zbl 0758.60073

[C] Chaumont, L. (1994). Processus de Lévy et Conditionnement. Thèse de Doctorat de l'Université Paris VI.

[C-T] Ciesielski, Z. & Taylor, S.J. (1962). First passage times and sojourn times for Brownian motion in space and the exact Hausdorff measure of the sample path. Trans. Amer. Math. Soc. 103 434-450. | Zbl 0121.13003

[Cs-F-R] Csáki, E., Földes, A. & Révész, P. (1987). On the maximum of a Wiener process and its location. Probab. Th. Rel. Fields 76 477-497. | Zbl 0611.60077

[G-S] Gruet, J.-C. & Shi, Z. (1996). The occupation time of Brownian motion in a ball. J. Theoretical Probab.9 429-445. | Zbl 0870.60072

[I-K] Ismail, M.E.H. & Kelker, D.H. (1979). Special functions, Stieltjes transforms and infinite divisibility. SIAM J. Math. Anal.10 884-901. | Zbl 0427.60021

[Ke] Kent, J. (1978). Some probabilistic properties of Bessel functions. Ann. Probab. 6 760-770. | MR 501378 | Zbl 0402.60080

[Kh] Khoshnevisan, D. (1995). The gap between the past supremum and the future infimum of a transient Bessel process. Séminaire de Probabilités XXIX(Eds.: J. Azéma, M. Emery, P.-A. Meyer & M. Yor. Lecture Notes in Mathematics 1613, pp. 220-230. Springer, Berlin. | Numdam | Zbl 0836.60083

[K-S] Kochen, S.B. & Stone, C.J. (1964). A note on the Borel-Cantelli lemma. Illinois J. Math.8 248-251. | Zbl 0139.35401

[M] Millar, P.W. (1977). Random times and decomposition theorems. In: "Probability": Proc. Symp. Pure Math. (Univ. Illinois, Urbana, 1976) 31 pp. 91-103. AMS, Providence, R.I. | MR 443109 | Zbl 0389.60058

[P] Pitman, J.W. (1975). One-dimensional Brownian motion and the three-dimen-sional Bessel process. Adv. Appl. Prob.7 511-526. | MR 375485 | Zbl 0332.60055

[R-Y] Revuz, D. & Yor, M. (1994). Continuous Martingales and Brownian Motion. (2nd edition) Springer, Berlin. | Zbl 0804.60001

[W1] Williams, D. (1970). Decomposing the Brownian path. Bull. Amer. Math. Soc.76 871-873. | MR 258130 | Zbl 0233.60066

[W2] Williams, D. (1974). Path decomposition and continuity of local time for one-dimensional diffusions, I. Proc. London Math. Soc. (3) 28 738-768. | MR 350881 | Zbl 0326.60093