Points of Positive Density for Smooth Functionals

Mireille Chaleyat-Maurel (Université de Paris VI)
David Nualart (Universitat de Barcelona)

Abstract


In this paper we show that the set of points where the density of a Wiener functional is strictly positive is an open connected set, assuming some regularity conditions.

Full Text: Download PDF | View PDF online (requires PDF plugin)

Pages: 1-8

Publication Date: December 2, 1997

DOI: 10.1214/EJP.v3-23

References

  1. G. Ben Arous and R. L'eandre, Annulation plate du noyau de la chaleur, C. R. Acad. Sci. Paris S'er. I Math. 312, (1991), 463--464. Math Review link
  2. S. Fang, Une in'egalit'e isop'erim'etrique sur l'espace de Wiener, Bull. Sci. Math. 112, (1988), 345--355. Math Review link
  3. S. Fang, On the Ornstein-Uhlenbeck process, Stochastics and Stochastics Rep. 46, (1994), 141-159.
  4. F. Hirsch and S. Song, Properties of the set of positivity for the density of a regular Wiener functional, Bull. Sciences Math. 121, (1997) 261-273.
  5. D. Nualart, The Malliavin calculus and related topics, Springer-Verlag, (1995). Math Review link
  6. D. Nualart, Analysis on Wiener space and anticipating stochastic calculus, Saint Flour lecture notes. To appear.


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.