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Duality and integral representation for excessive measures

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References

  1. Alfsen, E.M.: Compact Convex Sets and Boundary Integrals. Berlin Heidelberg New York: Springer 1971

    MATH  Google Scholar 

  2. Asimow, L., Ellis, A.I.: Convexity Theory and Its Applications in Functional Analysis. New York: Academic Press 1980

    MATH  Google Scholar 

  3. Ben Saad, H., Janßen, K.: Bernstein's theorem for completely excessive measures. Nagoya Math. J.119, 133–141 (1990)

    MathSciNet  Google Scholar 

  4. Beznea, L.: Ultrapotentials and positive eigenfunctions for an absolutely continuous resolvent of kernels. Nagoya Math. J.112, 125–142 (1988)

    MATH  MathSciNet  Google Scholar 

  5. Blumenthal, R.M.: A decomposition of excessive measures. In: Çinlar, E. et al. (eds.) Sem. Stochastic Processes 1985, pp. 1–8. Boston: Birkhäuser 1986

    Google Scholar 

  6. blumenthal, R.M., Getoor, R.K.: Markov Processes and Potential Theory. New York London: Academic Press 1968

    MATH  Google Scholar 

  7. Boboc, N., Bucur, Gh., Cornea, A.: Order and Convexity in Potential Theory:H-Cones. (Lect. Notes Math., vol 853) Berlin Heidelberg New York: Springer 1981

    MATH  Google Scholar 

  8. Cornea, A., Licea, G.: Order and Potential. Resolvent Families of Kernels. (Lect. Notes Math., vol. 494) Berlin Heidelberg New York: Springer 1975

    MATH  Google Scholar 

  9. Dellacherie, C., Meyer, P.A.: Probabilités et potentiel, Chap I–IV. Paris: Hermann 1975

    Google Scholar 

  10. Dellacherie, C., Meyer, P.A.: Probabilités et potentiel, Chap. IX–XI. Théorie discrète du potentiel. Paris: Hermann 1983

    Google Scholar 

  11. Dellacherie, C., Meyer, P.A.: Probabilités et potentiel, Chap. XII–XVI. Théorie du potentiel associée á une résolvante. Théorie des processus de Markov. Paris: Hermann 1987

    Google Scholar 

  12. Dubins, L.E., Freedman, D.A.: Exchangeable processes need not be mixtures of independent, identically distributed random variables. Z. Wahrscheinlichkeitstheor. Verw. Geb.48, 115–132 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  13. Dynkin, E.B.: Integral representation of excessive measures and excessive functions. Russ. Math. Surv.27(1), 43–84 (1972)

    Article  MATH  MathSciNet  Google Scholar 

  14. Dynkin, E.B.: Minimal excessive functions and measures. Trans. Am. Math. Soc.258, 217–244 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  15. Fitzsimmons, P.J., Maisonneuve, B.: Excessive measures and Markov processes with random birth and death. Z. Wahrscheinlichkeitstheor. Verw. Geb.72, 319–336 (1986)

    MATH  MathSciNet  Google Scholar 

  16. Getoor, R.K.: Markov Processes: Ray Processes and Right Processes. (Lect. Notes Math., vol. 440) Berlin Heidelberg New York: Springer 1975

    MATH  Google Scholar 

  17. Getoor, R.K.: Excessive Measures. Lecture Notes. Boston: Birkhäuser 1990

    MATH  Google Scholar 

  18. Getoor, R.K., Glover, J.: Riesz decompositions in Markov process theory. Trans. Am. Math. Soc.185, 107–132 (1984)

    Article  MathSciNet  Google Scholar 

  19. Getoor, R.K., Steffens, J.: The energy functional, balayage, and capacity. Ann. Inst. Henri Poincaré23, 321–357 (1987)

    MathSciNet  Google Scholar 

  20. Halmos, P.R.: Measure Theory. London: Van Nostrand 1950

    MATH  Google Scholar 

  21. Kerstan, J., Wakolbinger, A.: Ergodic decomposition of probability laws. Z. Wahrscheinlichkeitstheor. Verw. Geb.56, 399–414 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  22. Kunita, H., Watanabe, T.: Markov processes and Martin boundaries I. III. J. Math.9, 485–526 (1965)

    MATH  MathSciNet  Google Scholar 

  23. Kunita, H., Watanabe, T.: Some theorems concerning resolvents over locally compact spaces. In: Proc. 5th Berkeley Symp. II.2, pp. 131–164, Berkeley, Calif.: University of California Press 1967

    Google Scholar 

  24. Martin, R.S.: Minimal positive harmonic functions. Trans. Am. Math. Soc.49, 127–172 (1941)

    Google Scholar 

  25. Meyer, P.A.: Processus de Markov: la frontière de Martin. (Lect. Notes Math., vol. 77) Berlin Heidelberg New York: Berlin 1968

  26. Meyer, P.A.: Réprésentation intégrale des fonctions excessives. Résultats de Mokobodzki. In: Meyer, P.A. (ed.) Sém. Probab. V. (Lect. Notes Math., vol. 191, pp. 196–208) Berlin Heidelberg New York: Springer 1971

    Google Scholar 

  27. Meyer, P.A.: Le schéma de remplissage en temps continus d'après H. Rost. In: Meyer, P.A. (ed.) Sém. Probab. VI, pp. 130–150. Berlin Heidelberg New York: Springer 1972

    Google Scholar 

  28. Mokobodzki, G.: Réprésentation intégrale des fonctions surharmoniques au moyen des réduites. Ann. Inst. FourierXV, 103–112 (1965)

    MathSciNet  Google Scholar 

  29. Mokobodzki, G.: Structure des cônes de potentiels. Sémin. Bourbaki377 (1969/70)

  30. Mokobodzki, G.: Dualité formelle et réprésentation intégrale des fonctions excessives. Actes, Congrès Intern. Math. 1970,2, 531–535 (1971)

    MathSciNet  Google Scholar 

  31. Phelps, R.R.: Lectures on Choquet's Theorem. London: Van Nostrand 1966

    MATH  Google Scholar 

  32. Rogers, L.C.G.: Ito excursion theory via resolvents. Z. Wahrscheinlichkeitstheor. Verw. Geb.63, 237–255 (1983)

    Article  MATH  Google Scholar 

  33. Sharpe, M.: General Theory of Markov Processes. San Diego: Academic Press 1988

    MATH  Google Scholar 

  34. Steffens, J.: Excessive measures and the existence of right semigroups and processes. Trans. Am. Math. Soc.311, 267–290 (1989)

    Article  MATH  MathSciNet  Google Scholar 

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  1. Mathemathisches Institut, Universitätsstrasse 1, W-4000, Düsseldorf 1, Federal Republic of Germany

    J. Steffens

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Steffens, J. Duality and integral representation for excessive measures. Math Z 210, 495–512 (1992). https://doi.org/10.1007/BF02571810

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