Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Une propriété de continuité du temps local

Author: Lucien Chevalier
Journal: Proc. Amer. Math. Soc. 131 (2003), 933-936
MSC (2000): Primary 60G44
Published electronically: October 15, 2002
MathSciNet review: 1937439
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $L^0(M)$ denote the local time (at 0) associated with a martingale $M$. The aim of this note is to prove that the mapping $M \mapsto L^0(M)$ is continuous from $L^1$ into weak-$L^1$.

References [Enhancements On Off] (What's this?)

  • 1. J. Azéma et M. Yor. En guise d'introduction. Astérisque 52-53 (Temps locaux), Société mathématique de France (1978), 3-16.
  • 2. M. T. Barlow and M. Yor, (Semi-) martingale inequalities and local times, Z. Wahrsch. Verw. Gebiete 55 (1981), no. 3, 237–254. MR 608019, 10.1007/BF00532117
  • 3. D. L. Burkholder, Martingale transforms, Ann. Math. Statist. 37 (1966), 1494–1504. MR 0208647
  • 4. P. A. Meyer, Un cours sur les intégrales stochastiques, Séminaire de Probabilités, X (Seconde partie: Théorie des intégrales stochastiques, Univ. Strasbourg, Strasbourg, année universitaire 1974/1975), Springer, Berlin, 1976, pp. 245–400. Lecture Notes in Math., Vol. 511 (French). MR 0501332

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 60G44

Retrieve articles in all journals with MSC (2000): 60G44

Additional Information

Lucien Chevalier
Affiliation: Institut Fourier, U.M.R. 5582 C.N.R.S., Université Joseph Fourier, B.P. 74, 38402 Saint Martin d’Hères, France

Keywords: Martingales, continuity, local time
Received by editor(s): August 18, 2001
Published electronically: October 15, 2002
Communicated by: Claudia M. Neuhauser
Article copyright: © Copyright 2002 American Mathematical Society