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Parametric inference in Markov branching processes with time-dependent random immigration rate

Published online by Cambridge University Press:  14 July 2016

Helmut Pruscha
Helmut Pruscha*
Affiliation:
University of Munich
*
∗Postal address: University of Munich, Institute of Mathematics, Theresienstr. 39, D-8000 München, West Germany.
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Abstract

The present paper deals with continuous-time Markov branching processes allowing immigration. The immigration rate is allowed to be random and time-dependent where randomness may stem from an external source or from state-dependence. Unlike the traditional approach, we base the analysis of these processes on the theory of multivariate point processes. Using the tools of this theory, asymptotic results on parametric inference are derived for the subcritical case. In particular, the limit distributions of some parametric estimators and of Pearson-type statistics for testing simple and composite hypotheses are established.

Keywords

MULTIVARIATE POINT PROCESSESASYMPTOTIC PARAMETRIC INFERENCELIKELIHOOD RATIO TEST STATISTICS
Type
Research Papers
Information
Journal of Applied Probability , Volume 22 , Issue 3 , September 1985 , pp. 503 - 517
Copyright
Copyright © Applied Probability Trust 1985 

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