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)



Continuity of multidimensional Brownian local times

Author: Shey Shiung Sheu
Journal: Proc. Amer. Math. Soc. 114 (1992), 821-829
MSC: Primary 60J55; Secondary 60J65
MathSciNet review: 1091187
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The local time of a multidimensional semimartingle at a hypersurface will be defined via Tanaka's formula. One can define a certain distance between hypersurfaces so that the continuity properties of local time can be discussed when the underlying process is Brownian motion.

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

  • [1] R. Bass, Occupation times of $ d$-dimensional semimartingales, Sem. Stochastic Process. 1982, Birkhauser, Boston, 1983, pp. 51-76. MR 733665 (85j:60080)
  • [2] -, Joint continuity and representations of additive functionals of $ d$-dimensional Brownian motion, Stochastic. Process. Appl. 17 (1984), 211-227. MR 751203 (85j:60144)
  • [3] E. Csaki, M. Csörgö, A Földes, and P. Revesz, How big are the increments of the local time of a Wiener process?, Ann. Probab. 11 (1983), 593-608. MR 704546 (84i:60104)
  • [4] D. Freedman, Brownian motion and diffusion, Holden-Day, San Francisco, 1971. MR 0297016 (45:6074)
  • [5] N. Ikeda and S. Watanabe, Stochastic differential equations and diffusion processes, North-Holland, Amsterdam, 1981. MR 1011252 (90m:60069)
  • [6] K. Itô and H. P. McKean, Diffusion processes and their sample paths, Springer-Verlag, Berlin, 1965.
  • [7] F. Knight, Essential of Brownian motion and diffusion, Math. Surveys, vol. 18, Amer. Math. Soc. Providence, RI. 1981. MR 613983 (82m:60098)
  • [8] H. P. McKean, A Hölder condition for Brownian local time, J. Math. Kyoto Univ. Springer, Berlin (1962), 195-201. MR 0146902 (26:4421)
  • [9] P. Meyer, Un curs sur les integrals stochastiques, Sem. Probab., Lecture Notes in Math., vol. 511, (1976), 254-394. MR 0501332 (58:18721)
  • [10] D. Ray, Sojourn times of a diffusion process, Illinois J. Math. (1963), 615-630. MR 0156383 (27:6306)
  • [11] S. Sheu, A simple proof of Chevet's theorem, Bull. Inst. Math. Acad. Sinica, Vol 8, No. 1 (1980), 65-72. MR 562728 (81j:60063)
  • [12] M. Yor, Sur la transformee de Hilbert des temps locaux Browniens et une extension de la formule d'Itô, Sem. Probab., Lecture Notes in Math., vol. 920, Springer, Berlin (1981), 238-247. MR 658687 (83k:60093)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 60J55, 60J65

Retrieve articles in all journals with MSC: 60J55, 60J65

Additional Information

Keywords: Brownian motion, local time, Tanaka's formula, modulus of continuity
Article copyright: © Copyright 1992 American Mathematical Society

American Mathematical Society