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Functional laws for trimmed Lévy processes

Published online by Cambridge University Press:  15 September 2017

Boris Buchmann
Affiliation:
Australian National University
Yuguang F. Ipsen
Affiliation:
Australian National University and University of Melbourne
Ross Maller
Affiliation:
Australian National University

Abstract

Two different ways of trimming the sample path of a stochastic process in 𝔻[0, 1]: global ('trim as you go') trimming and record time ('lookback') trimming are analysed to find conditions for the corresponding operators to be continuous with respect to the (strong) J 1-topology. A key condition is that there should be no ties among the largest ordered jumps of the limit process. As an application of the theory, via the continuous mapping theorem, we prove limit theorems for trimmed Lévy processes, using the functional convergence of the underlying process to a stable process. The results are applied to a reinsurance ruin time problem.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 2017 

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References

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