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A representation for functionals of superprocesses via particle picture

Author

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  • Feldman, Raisa E.
  • Iyer, Srikanth K.

Abstract

A superprocess is a measure valued process arising as the limiting density of an infinite collection of particles undergoing branching and diffusion. It can also be defined as a measure valued Markov process with a specified semigroup. Using the latter definition and explicit moment calculations, Dynkin (1988) built multiple integrals for the superprocess. We show that the multiple integrals of the superprocess defined by Dynkin arise as weak limits of linear additive functionals built on the particle system.

Suggested Citation

  • Feldman, Raisa E. & Iyer, Srikanth K., 1996. "A representation for functionals of superprocesses via particle picture," Stochastic Processes and their Applications, Elsevier, vol. 64(2), pages 173-186, November.
    • Handle: RePEc:eee:spapps:v:64:y:1996:i:2:p:173-186
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    References listed on IDEAS

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    1. Adler, Robert J. & Epstein, R., 1987. "Some central limit theorems for Markov paths and some properties of Gaussian random fields," Stochastic Processes and their Applications, Elsevier, vol. 24(2), pages 157-202, May.
    2. Adler, Robert J. & Lewin, Marica, 1992. "Local time and Tanaka formulae for super Brownian and super stable processes," Stochastic Processes and their Applications, Elsevier, vol. 41(1), pages 45-67, May.
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    Cited by:

    1. Robert J. Adler & Srikanth K. Iyer, 2001. "On Changes of Measure for Super Brownian Motion," Journal of Theoretical Probability, Springer, vol. 14(2), pages 527-557, April.

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