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Potential Analysis

, Volume 7, Issue 3, pp 623–659 | Cite as

Points of Positive Density for the Solution to a Hyperbolic SPDE

  • Annie Millet
  • Marta Sanz-Solé
Article

Abstract

Using a slightly modified version of Aida–Kusuoka–Stroock's characterization of the points of strictly positive density for an arbitrary Wiener functional, we extend the theorem of Ben Arous–Léandre to solutions of hyperbolic SPDE's. Thus we show that the density f of the law of Xz is positive at y if and only if y can be achieved as Sz(h), where S(h) is the controlled equation corresponding to an element h of the Cameron–Martin space, and S(.)z is a submersion at h. The proof depends on a convergence result for a sequence Xn,ξ of perturbed processes (defined in terms of a non homogeneous linear interpolation of the Brownian sheet) to the solution Xξ of the corresponding perturbed SPDE.

Hyperbolic SPDE Brownian sheet Cameron Martin space density. 

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Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • Annie Millet
  • Marta Sanz-Solé

There are no affiliations available

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