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Some Remarks on Capacities

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Seminar on Stochastic Processes, 1986

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

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Abstract

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.

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References

  1. R.M. Blumenthal: A decomposition of excessive measures. To appear in Seminar on Stochastic Processes 1985.

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  2. C. Dellacherie, P.A. Meyer: Probabilités et Potentiel. Vol. IV, chap. XII/XIII, preprint.

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  3. P.J. Fitzsimmons, B. Maisonneuve: Excessive measures and Markov processes with random birth and death. Probab. Th. Rel. Fields 72, 319–336, (1986).

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  4. R.K. Getoor: Capacity theory and weak duality. Seminar on Stochastic Processes 1983, 97–130. Birkhäuser, Boston 1984.

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  5. R.K. Getoor, M.J. Sharpe: Naturality, standardness, and weak duality for Markov processes. Z. Wahrscheinlichkeitstheorie verw. Geb. 67, 1–62 (1984).

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  6. R.K. Getoor, J. Steffens: Capacity theory without duality. Submitted to Z. Wahrscheinlichkeitstheorie verw. Geb., accepted by Probab. Th. Rel. Fields.

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  7. R.K. Getoor, J. Steffens: The energy functional, balayage, and capacity. In preparation.

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  8. G.A. Hunt: Markov processes and potentials III. Ill. J. Math. 2, 151–213 (1958).

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  9. P.A. Meyer: Note sur l’interpretation des mesures d’équilibre. Séminaire de Probabilité VII, 210–216 (1973).

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Author information

Authors and Affiliations

  1. Institut für Statistik und Dokumentation, Universität Düsseldorf, Universitätsstr. 1, D-4000, Düsseldorf 1, West-Germany

    Jutta Steffens

Authors
  1. Jutta Steffens
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Editor information

Editors and Affiliations

  1. Civil Engineering Department, Princeton University, 08544, Princeton, NJ, USA

    E. Çinlar

  2. Department of Mathematics, Stanford University, 94305, Stanford, CA, USA

    K. L. Chung

  3. Department of Mathematics, University of California, 92093, La Jolla, CA, USA

    R. K. Getoor

  4. Department of Mathematics, University of Florida, 32611, Gainesville, FL, USA

    J. Glover

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© 1987 Birkhäuser Boston

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Steffens, J. (1987). Some Remarks on Capacities. In: Çinlar, E., Chung, K.L., Getoor, R.K., Glover, J. (eds) Seminar on Stochastic Processes, 1986. Progress in Probability and Statistics, vol 13. Birkhäuser Boston. https://doi.org/10.1007/978-1-4684-6751-2_14

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  • DOI: https://doi.org/10.1007/978-1-4684-6751-2_14

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-1-4684-6753-6

  • Online ISBN: 978-1-4684-6751-2

  • eBook Packages: Springer Book Archive

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