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Regularity Properties of a Supercritical Superprocess

  • S. E. Kuznetsov
Part of the Progress in Probability book series (PRPR, volume 34)

Abstract

The objective of this chapter is to derive the regularity properties of a superprocess from those of the spatial process. We assume that the spatial process ζ is a right (nonhomogeneous) Markov process in a Luzin state space and we prove that a superprocess over ζ can be chosen right if the first moments of the total mass X t (E) are finite.

Keywords

Markov Process Spatial Process Regularity Property London Mathematical Society Lecture Note Mathematical Society Lecture Note Series 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [DM]
    C. Dellacherie and P.-A. Meyer, Probabilités et Potentiel, Hermann, Paris, 1975, 1980, 1983, 1987.MATHGoogle Scholar
  2. [Dyl]
    E.B. Dynkin, The initial and final behavior of trajectories of Markov processes, Russian Math. Surveys 26,4 (1971), 165–185; Reprinted in “London Mathematical Society Lecture Note Series 54,” 123–143, Cambridge Univ. Press, London, New York.MathSciNetCrossRefGoogle Scholar
  3. [Dy2]
    E.B. Dynkin, Integral representation of excessive measures and excessive functions, Russian Math. Surveys 27,1 (1972), 43–84; Reprinted in “London Mathematical Society Lecture Note Series 54,” 145–186, Cambridge Univ. Press, London, New York.MathSciNetCrossRefMATHGoogle Scholar
  4. [Dy3]
    E.B. Dynkin, Regular Markov processes, Russian Math. Surveys 28,2 (1973), 33–64; Reprinted in “London Mathematical Society Lecture Note Series 54,” 187–218, Cambridge Univ. Press, London, New York.MathSciNetCrossRefMATHGoogle Scholar
  5. [Dy4]
    E.B. Dynkin, Sufficient statistics and extreme points, Annals of Probability 6 (1978), 705–730.MathSciNetCrossRefMATHGoogle Scholar
  6. [Dy5]
    E.B. Dynkin, Regular transition functions and regular superprocesses, Trans. Amer. Math. Society 316 (1989), 623–634.MathSciNetCrossRefMATHGoogle Scholar
  7. [Dy6]
    E.B. Dynkin, Birth delay of a Markov process and the stopping distributions for regular processes, Probab. Theory Relat. Fields 94 (1993), 399–411.MathSciNetCrossRefMATHGoogle Scholar
  8. [Dy7]
    E.B. Dynkin, On regularity of superprocesses, Probab. Theory Relat. Fields 95 (1993), 263–281.MathSciNetCrossRefMATHGoogle Scholar
  9. [Dy8]
    E.B. Dynkin, An Introduction to Branching Measure-Valued Processes, Centre de Recherches Mathématiques of Université de Montreal and American Mathematical Society, 1994 (forthcoming book).Google Scholar
  10. [F]
    P.J. Fitzsimmons, Construction and regularity of measure-valued Markov branching processes, Israel J. Math. 64 (1988), 337–361.MathSciNetCrossRefMATHGoogle Scholar
  11. [K]
    K. Kuratowski, Topology, Academic Press, New York, 1967.Google Scholar
  12. [Ku]
    S.E. Kuznetsov, Nonhomogeneous Markov processes, Sovremennye Problemy Matematiki 20 (1982), 37–178, VINITI, Moscow (Russian); English translation in J. Soviet Math. 25 (1984), 1380–1498.Google Scholar

Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • S. E. Kuznetsov
    • 1
  1. 1.Central Institute for Economics and Mathematics of The Russian Academy of SciencesMoscowRussia

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