Some Characterizations of Mixed Poisson Processes
D. P. Lyberopoulos, N. D. Macheras (University of Piraeus,, Department of Statistics, Insurance Science, Greece)
TL;DR
This paper characterizes mixed Poisson processes using disintegrations and explores their properties through claim interarrival processes, martingales, and claim measures.
Contribution
It provides new characterizations of mixed Poisson processes based on disintegrations and related stochastic process properties.
Findings
Characterization of mixed Poisson processes via disintegrations
Connections to claim interarrival processes and martingales
Additional properties of claim measures
Abstract
A characterization of mixed Poisson processes in terms of disintegrations is proven. As a consequence some further characterizations of such processes via claim interarrival processes, martingales and claim measures are obtained. Some revisions are required
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Taxonomy
TopicsProbability and Risk Models · Statistical Methods in Clinical Trials