On tightness of probability measures on Skorokhod spaces.

• Author(s) / Creator(s)

  • Kouritzin, Michael

• 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.

• Date created

  2013-09-10

• Subjects / Keywords

  • Tightness
  • Modulus of Continuity
  • Skorokhod topology
  • Measure-valued process
  • Compact Containment
  • Strassen-Dudley coupling

• Type of Item

  Article (Draft / Submitted)

• DOI

  https://doi.org/10.7939/R3F47H12J

• License

  © 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.