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Measure-valued Markov branching processes conditioned on non-extinction

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Abstract

We consider a particular class of measure-valued Markov branching processes that are constructed as “superprocesses” over some underlying Markov process. Such a processX dies out almost surely, so we introduce various conditioning schemes which keepX alive at large times. Under suitable hypotheses, which include the convergence of the semigroup for the underlying process to some limiting probability measureν, we show that the conditional distribution oft −1 X t converges to that ofZν ast → ∞, whereZ is some strictly positive, real random variable.

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Authors and Affiliations

  1. Department of Statistics, University of California at Berkeley, 367 Evans Hall, 94720, Berkeley, CA, USA

    Steven N. Evans

  2. Department of Mathematics, University of British Columbia, V6T 1Y4, Vancouver, BC, Canada

    Edwin Perkins

Authors
  1. Steven N. Evans
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  2. Edwin Perkins
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Additional information

Research supported in part by NSF grant DMS 8701212.

Research supported in part by an NSERC operating grant.

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Evans, S.N., Perkins, E. Measure-valued Markov branching processes conditioned on non-extinction. Israel J. Math. 71, 329–337 (1990). https://doi.org/10.1007/BF02773751

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  • DOI: https://doi.org/10.1007/BF02773751

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