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Useful Martingales for Stochastic Storage Processes with Lévy-Type Input
Published online by Cambridge University Press: 30 January 2018
Abstract
In this paper we generalize the martingale of Kella and Whitt to the setting of Lévy-type processes and show that the (local) martingales obtained are in fact square-integrable martingales which upon dividing by the time index converge to zero almost surely and in L2. The reflected Lévy-type process is considered as an example.
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- Research Article
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- © Applied Probability Trust
Footnotes
Supported in part by grant 434/09 from the Israel Science Foundation, the Vigevani Chair in Statistics, and visitor grant no. 040.11.257 from The Netherlands Organisation for Scientific Research.
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