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On tightness of probability measures on Skorokhod spaces


Author: Michael A. Kouritzin
Journal: Trans. Amer. Math. Soc. 368 (2016), 5675-5700
MSC (2010): Primary 60B05; Secondary 60B10
Published electronically: November 16, 2015
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Abstract: The equivalences to and the connections between the modulus-of-continuity condition, compact containment and tightness on $ D_{E}[a,b]$ with $ a<b$ are studied. The results within are tools for establishing tightness for probability measures on $ D_E[a,b]$ that generalize and simplify prevailing results in the cases that $ E$ is a metric space, nuclear space dual or, more generally, a completely regular topological space. Applications include establishing weak convergence to martingale problems, the long-time typical behavior of nonlinear filters and particle approximation of cadlag probability-measure-valued processes. This particle approximation is studied herein, where the distribution of the particles is the underlying measure-valued process at an arbitrarily fine discrete mesh of points.


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Additional Information

Michael A. Kouritzin
Affiliation: Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1, Canada
Email: michaelk@ualberta.ca

DOI: https://doi.org/10.1090/tran/6522
Keywords: Tightness, Skorokhod topology, compact containment, modulus of continuity, measure-valued process, exchangeable particles, Strassen-Dudley coupling
Received by editor(s): September 10, 2013
Received by editor(s) in revised form: July 17, 2014
Published electronically: November 16, 2015
Article copyright: © Copyright 2015 American Mathematical Society