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Multiplicative functionals and the stable topology

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Multiplicative functionals and the stable topology SÉMINAIRE DE PROBABILITÉS (STRASBOURG) JOHN R. BAXTER RAFAEL V. CHACON Multiplicative functionals and the stable topology Séminaire de probabilités (Strasbourg), tome 23 (1989), p. 475-489. <> © Springer-Verlag, Berlin Heidelberg New York, 1989, tous droits réservés. L’accès aux archives du séminaire de probabilités (Strasbourg) (http://www-irma., implique l’accord avec les conditions gé- nérales d’utilisation ( Toute utilisation commer- ciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques Multiplicative Functionals and the Stable Topology J.R. Baxter and R.V.Chacon Department of Mathematics, University of Minnesota, Minneapolis, MN 5455, and Department of Mathematics, University of British Columbia, Vancouver, BC V6T lY4 Abstract The notion of a randomized stopping time has various applications in probability. Here it is shown that stable compactness for randomized stopping times is especially useful in the case of randomized stopping times which happen to be multiplicative functionals . The general results on convergence of multiplicative functionals are used to simplify the analysis of the convergence of diffusions in regions with many small holes. 1. Introduction The stable topology for stopping times and time changes was originally developed as an aid to various constructions in the study of Markov processes and martingales [2],[14]. It was later used in the study of optimal stopping problems [11]. More recently [3],[4] it has proved useful in studying the behaviour of a diffusion in a region with many small holes (see Section 7). Some additional properties of stable c

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