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Convergence for Reflecting Boundaries, Singular Control and Ergodic Cost Problems

  • Harold J. Kushner
  • Paul Dupuis
Part of the Stochastic Modelling and Applied Probability book series (SMAP, volume 24)

Abstract

The development of the convergence proofs of Chapter 10 is continued, but applied to the problem classes of Chapters 7 and 8. The reflecting boundary and discounted cost problem is covered in Section 11.1. The primary mathematical difficulty with which we must contend is the proof of tightness of the “reflecting process.” The problem is avoided by use of a time rescaling method, under which all the processes are tight. After proving the weak convergence of the rescaled processes and characterizing the limits, the rescaling is inverted to obtain the desired results. This “inversion” is possible due to the conditions imposed on the allowable reflection directions. The time rescaling idea appears to be a rather powerful tool.

Keywords

Invariant Measure Weak Convergence Weak Sense Convergent Subsequence Admissible Control 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Harold J. Kushner
    • 1
  • Paul Dupuis
    • 1
  1. 1.Division of Applied MathematicsBrown UniversityProvidenceUSA

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