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