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

Abstract

Subordinators are much older objects than regenerative sets, as defined by Hoffmann — Jorgensen [3], and it is natural to try to deduce the structure of the second from the structure of the first. This was done in [5] through the existence of a local time for a perfect regenerative set.

This work was supported by AFOSR contract N° F49620-79-C-0080 while the author was visiting Northwestern University, Evanston, in August 1979.

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References

  1. R.M. Blumenthal and R.K. Getoor. — Markov Processes and Potential Theory, Academic Press, New-York, 1968.

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  2. E. Çinlar and B. Maisonneuve. — The image of a markov additive process, (to appear).

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  3. J. Hoffmann-Jorgensen. — Markov sets, Mathematica Scandinavia, 24, fasc. 2, 0. 969 ).

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  4. B. Maisonneuve and PH. Morando. — Temps local d’un ensemble régénératif, Séminaire de Probabilités IV. Lecture Notes in Mathematics, Springer, Berlin, 124, 1970.

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  5. B. Maisonneuve. — Ensembles régénératifs, temps locaux et subordinateurs, Séminaire de Probabilités V. Lecture Notes in Mathematics, Springer, Berlin, 191, 1971.

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  6. B. Maisonneuve. — Systèmes Régénératifs, Astérisque 15, S.M.F., 1974.

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  7. P.A. Meyer. — Ensembles régénératifs, d’après Hoffmann- Jorgensen, Séminaire de Probabilités IV. Lecture Notes in Mathematics, Springer, Berlin, 124, 1970.

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© 1987 Birkhäuser Boston

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Maisonneuve, B. (1987). Subordinators Regenerated. 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_11

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  • DOI: https://doi.org/10.1007/978-1-4684-6751-2_11

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-1-4684-6753-6

  • Online ISBN: 978-1-4684-6751-2

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