Useful Martingales for Stochastic Storage Processes with Lévy-Type Input

Offer Kella; Onno Boxma

doi:10.1239/jap/1371648952

Useful Martingales for Stochastic Storage Processes with Lévy-Type Input

Offer Kella
, Onno Boxma

Department of Statistics

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

In this paper we generalize the martingale of Kella and Whitt to the setting of Leévy-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 Leévy-type process is considered as an example.

Original language	English
Pages (from-to)	439-449
Number of pages	11
Journal	Journal of Applied Probability
Volume	50
Issue number	2
DOIs	https://doi.org/10.1239/jap/1371648952
State	Published - Jun 2013

Keywords

Kella-whitt martingale
Leévy storage system
Leévy-type process

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10.1239/jap/1371648952

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abstract = "In this paper we generalize the martingale of Kella and Whitt to the setting of Le{\'e}vy-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 Le{\'e}vy-type process is considered as an example.",

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AB - In this paper we generalize the martingale of Kella and Whitt to the setting of Leévy-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 Leévy-type process is considered as an example.

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KW - Leévy storage system

KW - Leévy-type process

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Useful Martingales for Stochastic Storage Processes with Lévy-Type Input

Abstract

Keywords

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