On the tails of the supremum and the quadratic variation of strictly local martingales

Kenneth David Elworthy; Xu-Mei Li; Marc Yor

Séminaire de probabilités de Strasbourg (1997)

  • Volume: 31, page 113-125

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Elworthy, Kenneth David, Li, Xu-Mei, and Yor, Marc. "On the tails of the supremum and the quadratic variation of strictly local martingales." Séminaire de probabilités de Strasbourg 31 (1997): 113-125. <http://eudml.org/doc/113946>.

@article{Elworthy1997,
author = {Elworthy, Kenneth David, Li, Xu-Mei, Yor, Marc},
journal = {Séminaire de probabilités de Strasbourg},
keywords = {local martingale; tails of distribution; transient diffusion; Bessel process; Tauberian theorem},
language = {fre},
pages = {113-125},
publisher = {Springer - Lecture Notes in Mathematics},
title = {On the tails of the supremum and the quadratic variation of strictly local martingales},
url = {http://eudml.org/doc/113946},
volume = {31},
year = {1997},
}

TY - JOUR
AU - Elworthy, Kenneth David
AU - Li, Xu-Mei
AU - Yor, Marc
TI - On the tails of the supremum and the quadratic variation of strictly local martingales
JO - Séminaire de probabilités de Strasbourg
PY - 1997
PB - Springer - Lecture Notes in Mathematics
VL - 31
SP - 113
EP - 125
LA - fre
KW - local martingale; tails of distribution; transient diffusion; Bessel process; Tauberian theorem
UR - http://eudml.org/doc/113946
ER -

References

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  1. [0] W. Feller : An Introduction to probability and its Applications. Volume 2 - Wiley (1970). 
  2. [1] J.F. Le Gall : Sur la saucisse de Wiener et les points multiples du mouvement brownien. The Annals of Proba.14, (4), p. 1219-1244 (1986). Zbl0621.60083MR866344
  3. [2] N.N. Lebedev : Special Functions and their Applications. Dover Publications (1972). Zbl0271.33001MR350075
  4. [3] J.W. Pitman, M. Yor : Bessel processes and infinitely divisible laws. In : Stochastic Integrals, ed : D. Williams, Durham Conference 1980. Lect. Notes in Maths.851, p. 285-370. Springer (1981). Zbl0469.60076MR620995
  5. [4] J.W. Pitman, M. Yor : A decomposition of Bessel bridges. Zeit. für Wahr., 59, p. 425-457 (1982). Zbl0484.60062MR656509
  6. [5] F. Spitzer : Some theorems about 2-dimensional Brownian motion. Trans. Amer Math. Soc.87, p. 187-197 (1958). Zbl0089.13601MR104296
  7. [6] G.N. Watson : A treatise of the theory of Bessel functions. Cambridge Univ. Press (1966). Zbl0174.36202
  8. [7] W. Werner : Sur l'ensemble des points autour desquels le mouvement brownien tourne beaucoup. Prob. Th. Rel. Fields99, p. 111-142 (1994). Zbl0799.60074MR1273744
  9. [8] M. Yor : Loi de l'indice du lacet brownien et distribution de Hartman-Watson. Zeit. für Wahr., 53, p. 71-95 (1980). Zbl0436.60057MR576898
  10. [9] K.D. Elworthy, X.M. Li, M. Yor : The importance of strictly local martingales ; applications to radial Ornstein-Uhlenbeck process. Preprint (1996). MR1725406
  11. [10] L.I. Galtchouk, A.A. Novikov : Wald equation ; discrete time case. Preprint (March 1994). Strasbourg University. 

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