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Branching measure-valued processes
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  • Published: March 1994

Branching measure-valued processes

  • E. B. Dynkin1,
  • S. E. Kuznetsov2 &
  • A. V. Skorokhod3 

Probability Theory and Related Fields volume 99, pages 55–96 (1994)Cite this article

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Summary

The objective of this paper is to investigate the structure of a general subcritical branching measure-valued processX subject to the usual regularity conditions. We prove that, if the second moments of the total massX t (E) are finite, thenX is a superprocess and we give an explicit expression of the branching characteristicsQ andl in terms of the continuous martingale component of the total massX t (E) and the Lévy measure (jumps compensator) ofX.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Cornell University, White Hall, 14853-7901, Ithaca, NY, USA

    E. B. Dynkin

  2. Central Econ.-Math. Institute, Russian Academy of Sciences, 32 Krasikowa, 117418, Moscow, Russia

    S. E. Kuznetsov

  3. Mathematical Institute, Ukrainian Academy of Sciences, 3 Repina, Kiev, Ukraine

    A. V. Skorokhod

Authors
  1. E. B. Dynkin
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  2. S. E. Kuznetsov
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  3. A. V. Skorokhod
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Additional information

Partially supported by National Science Foundation Grant DMS-9146347 and by The US Army Research Office through the Mathematical Sciences Institute at Cornell University

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Dynkin, E.B., Kuznetsov, S.E. & Skorokhod, A.V. Branching measure-valued processes. Probab. Th. Rel. Fields 99, 55–96 (1994). https://doi.org/10.1007/BF01199590

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  • Received: 26 August 1992

  • Revised: 24 May 1993

  • Issue Date: March 1994

  • DOI: https://doi.org/10.1007/BF01199590

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Mathematics Subject Classification 1991

  • 60J80
  • 60J25
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