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Statistical Models for Birth and Death on a Flow: Local Absolute Continuity and Likelihood Ratio Processes

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  • R. Höpfner
  • E. Löcherbach

Abstract

ABSTRACT. We consider statistical models for birth and death on a flow. We give necessary and sufficient conditions for local absolute continuity between laws of such processes on a suitable canonical path space, and prove that likelihood ratio processes do have a very simple form. Key tools are criteria for local absolute continuity of laws of l‐point motions–for arbitrary l–on stochastic flows, under an assumption on the structure of infinitesimalcovariances.

Suggested Citation

  • R. Höpfner & E. Löcherbach, 1999. "Statistical Models for Birth and Death on a Flow: Local Absolute Continuity and Likelihood Ratio Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(1), pages 107-128, March.
    • Handle: RePEc:bla:scjsta:v:26:y:1999:i:1:p:107-128
    DOI: 10.1111/1467-9469.00140
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    Cited by:

    1. E. Löcherbach, 2002. "Likelihood Ratio Processes for Markovian Particle Systems with Killing and Jumps," Statistical Inference for Stochastic Processes, Springer, vol. 5(2), pages 153-177, May.
    2. R. HÖpfner & E. LÖcherbach, 1998. "Birth and Death on a Flow: Local Time and Estimation of a Position‐Dependent Death Rate," Statistical Inference for Stochastic Processes, Springer, vol. 1(3), pages 225-243, October.

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