A supermartingale characterization of sets of stochastic integrals and applications

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Abstract

A supermartingale characterization of sets of stochastic integrals is given along with its applications to control and diffusion approximation. The characterization is convenient for passing to the limit. Under natural conditions it is proved that the set of distributions of controlled diffusion processes is convex and compact.

Original languageEnglish (US)
Pages (from-to)521-552
Number of pages32
JournalProbability Theory and Related Fields
Volume123
Issue number4
DOIs
StatePublished - Aug 1 2002

Keywords

  • Diffusion approximation
  • Optimal control
  • Stochastic differential equations
  • Weak convergence

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