Some Remarks on Capacities

  • Jutta Steffens
Part of the Progress in Probability and Statistics book series (PRPR, volume 13)


In the paper “Capacity theory without duality” [6] a purely probabilistic notion of capacity relative to a general right process and an excessive measure was introduced by means of the corresponding stationary process.


Invariant Part Capacity Theory Excessive Measure Excessive Part Analogous Kernel 


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  1. [1]
    R.M. Blumenthal: A decomposition of excessive measures. To appear in Seminar on Stochastic Processes 1985.Google Scholar
  2. [2]
    C. Dellacherie, P.A. Meyer: Probabilités et Potentiel. Vol. IV, chap. XII/XIII, preprint.Google Scholar
  3. [3]
    P.J. Fitzsimmons, B. Maisonneuve: Excessive measures and Markov processes with random birth and death. Probab. Th. Rel. Fields 72, 319–336, (1986).MathSciNetMATHCrossRefGoogle Scholar
  4. [4]
    R.K. Getoor: Capacity theory and weak duality. Seminar on Stochastic Processes 1983, 97–130. Birkhäuser, Boston 1984.Google Scholar
  5. [5]
    R.K. Getoor, M.J. Sharpe: Naturality, standardness, and weak duality for Markov processes. Z. Wahrscheinlichkeitstheorie verw. Geb. 67, 1–62 (1984).MathSciNetMATHCrossRefGoogle Scholar
  6. [6]
    R.K. Getoor, J. Steffens: Capacity theory without duality. Submitted to Z. Wahrscheinlichkeitstheorie verw. Geb., accepted by Probab. Th. Rel. Fields.Google Scholar
  7. [7]
    R.K. Getoor, J. Steffens: The energy functional, balayage, and capacity. In preparation.Google Scholar
  8. [8]
    G.A. Hunt: Markov processes and potentials III. Ill. J. Math. 2, 151–213 (1958).Google Scholar
  9. [9]
    P.A. Meyer: Note sur l’interpretation des mesures d’équilibre. Séminaire de Probabilité VII, 210–216 (1973).Google Scholar

Copyright information

© Birkhäuser Boston 1987

Authors and Affiliations

  • Jutta Steffens
    • 1
  1. 1.Institut für Statistik und DokumentationUniversität DüsseldorfDüsseldorf 1West-Germany

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