Invariant Measures and the Ergodic Problem

  • Harold J. Kushner
Part of the Stochastic Modelling and Applied Probability book series (SMAP, volume 47)


A major concern in heavy traffic analysis is the long-time behavior of the physical systems, whether uncontrolled, controlled or optimally controlled, as well as the long time behavior of the weak-sense limit processes. The ergodic cost (or average cost per unit time over a long time interval) problem is particularly important in applications of heavy traffic analysis to communications systems. Due to their high speed, they tend to reach their new “steady states” rapidly as the operating conditions change.


Lebesgue Measure Invariant Measure Wiener Process Standard Wiener Process Optimal Feedback Control 
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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

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

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