Journal of Applied Probability

Useful martingales for stochastic storage processes with Lévy-type input

Offer Kella and Onno Boxma

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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.

Article information

Source
J. Appl. Probab., Volume 50, Number 2 (2013), 439-449.

Dates
First available in Project Euclid: 19 June 2013

Permanent link to this document
https://projecteuclid.org/euclid.jap/1371648952

Digital Object Identifier
doi:10.1239/jap/1371648952

Mathematical Reviews number (MathSciNet)
MR3102491

Zentralblatt MATH identifier
1274.60272

Subjects
Primary: 60K25: Queueing theory [See also 68M20, 90B22] 60K37: Processes in random environments 60K30: Applications (congestion, allocation, storage, traffic, etc.) [See also 90Bxx] 60H30: Applications of stochastic analysis (to PDE, etc.)

Keywords
Lévy-type process Lévy storage system Kella-Whitt martingale

Citation

Kella, Offer; Boxma, Onno. Useful martingales for stochastic storage processes with Lévy-type input. J. Appl. Probab. 50 (2013), no. 2, 439--449. doi:10.1239/jap/1371648952. https://projecteuclid.org/euclid.jap/1371648952


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