On Some Properties of Universal Sigma-Finite Measures Associated with a Remarkable Class of Submartingales

  • Joseph Najnudel

    Universität Zürich, Switzerland
  • Ashkan Nikeghbali

    Universität Zürich, Switzerland

Abstract

In a previous work, we associated with any submartingale of class , defined on a filtered probability space satisfying some technical conditions, a -finite measure on , such that for all , and for all events :

where is the last hitting time of zero by the process . In this paper we establish some remarkable properties of this measure from which we also deduce a universal class of penalisation results of the probability measure with respect to a large class of functionals. The measure appears to be the unifying object in these problems.

Cite this article

Joseph Najnudel, Ashkan Nikeghbali, On Some Properties of Universal Sigma-Finite Measures Associated with a Remarkable Class of Submartingales. Publ. Res. Inst. Math. Sci. 47 (2011), no. 4, pp. 911–936

DOI 10.2977/PRIMS/56