On tightness of probability measures on Skorokhod spaces.

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  • The equivalences to and the connections between the modulus-of-continuity condition, compact containment and tightness on DE[a, b] with a < b are studied. The results within are tools for establishing tightness for probability measures on DE[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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    Article (Draft / Submitted)
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    © 2013 Michael Kouritzin. This version of this article is open access and can be downloaded and shared. The original author(s) and source must be cited.