Convergence in Energy and the Sector Condition for Markov Processes

  • Z. R. Pop-Stojanovic
Part of the Progress in Probability and Statistics book series (PRPR, volume 9)


In an earlier paper [2], p. 148, dealing with properties of the energy of Markov processes, M. Rao and the author have shown that the so-called sector condition introduced by M. L. Silverstein [4], p. 17, is sufficient for the regularity of the limit potential. This paper will explain the meaning of the sector condition in relation to convergence in energy for certain classes of Markov processes.


Markov Process Cauchy Sequence Sector Condition Admissible Function Resolvent Operator 
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  1. [1]
    R.M. Blumenthal and R.K. rgetoor. Markov Processes and Potential Theory. Academic Press, New York, 1968.MATHGoogle Scholar
  2. [2]
    Z.R. POP-STOJANOVIC and MURALI RAO. Some Results on Energy. Seminar on Stochastic Processes 1981, pp. 135–150. Birkhäuser, Boston, 1981.CrossRefGoogle Scholar
  3. [3]
    z.R. Pop-Stojanovic and Murali Rao. Remarks on Energy. Seminar on Stochastic Processes 1982, pp. 229–235, Birkhäuser, Boston, 1983. Google Scholar
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    M.L. Silverstein. The Sector Condition implies that semipolar sets are quasi-polar. Z. Wahrscheinlichkeitstheorie verw. Gebiete, 41 (1977), 13–33.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Birkhäuser Boston, Inc. 1986

Authors and Affiliations

  • Z. R. Pop-Stojanovic
    • 1
  1. 1.Department of MathematicsUniversity of FloridaGainesvilleUSA

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