How long does it take a transient Bessel process to reach its future infimum?

Zhan Shi

Séminaire de probabilités de Strasbourg (1996)

  • Volume: 30, page 207-217

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Shi, Zhan. "How long does it take a transient Bessel process to reach its future infimum?." Séminaire de probabilités de Strasbourg 30 (1996): 207-217. <http://eudml.org/doc/113928>.

@article{Shi1996,
author = {Shi, Zhan},
journal = {Séminaire de probabilités de Strasbourg},
keywords = {transient Bessel process; integral criterion; upper functions},
language = {fre},
pages = {207-217},
publisher = {Springer - Lecture Notes in Mathematics},
title = {How long does it take a transient Bessel process to reach its future infimum?},
url = {http://eudml.org/doc/113928},
volume = {30},
year = {1996},
}

TY - JOUR
AU - Shi, Zhan
TI - How long does it take a transient Bessel process to reach its future infimum?
JO - Séminaire de probabilités de Strasbourg
PY - 1996
PB - Springer - Lecture Notes in Mathematics
VL - 30
SP - 207
EP - 217
LA - fre
KW - transient Bessel process; integral criterion; upper functions
UR - http://eudml.org/doc/113928
ER -

References

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  2. [C] Chaumont, L. (1994). Processus de Lévy et Conditionnement. Thèse de Doctorat de l'Université Paris VI. 
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  6. [I-K] Ismail, M.E.H. & Kelker, D.H. (1979). Special functions, Stieltjes transforms and infinite divisibility. SIAM J. Math. Anal.10884-901. Zbl0427.60021
  7. [Ke] Kent, J. (1978). Some probabilistic properties of Bessel functions. Ann. Probab.6760-770. Zbl0402.60080MR501378
  8. [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 Mathematics1613, pp. 220-230. Springer, Berlin. Zbl0836.60083
  9. [K-S] Kochen, S.B. & Stone, C.J. (1964). A note on the Borel-Cantelli lemma. Illinois J. Math.8248-251. Zbl0139.35401
  10. [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. Zbl0389.60058MR443109
  11. [P] Pitman, J.W. (1975). One-dimensional Brownian motion and the three-dimen-sional Bessel process. Adv. Appl. Prob.7511-526. Zbl0332.60055MR375485
  12. [R-Y] Revuz, D. & Yor, M. (1994). Continuous Martingales and Brownian Motion. (2nd edition) Springer, Berlin. Zbl0804.60001
  13. [W1] Williams, D. (1970). Decomposing the Brownian path. Bull. Amer. Math. Soc.76871-873. Zbl0233.60066MR258130
  14. [W2] Williams, D. (1974). Path decomposition and continuity of local time for one-dimensional diffusions, I. Proc. London Math. Soc. (3) 28738-768. Zbl0326.60093MR350881

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