Journal of Applied Probability

A piecewise linear stochastic differential equation driven by a Lévy process

Josh Reed and Bert Zwart

Abstract

We consider a stochastic differential equation (SDE) with piecewise linear drift driven by a spectrally one-sided Lévy process. We show that this SDE has some connections with queueing and storage models, and we use this observation to obtain the invariant distribution.

Article information

Source
J. Appl. Probab., Volume 48A (2011), 109-119.

Dates
First available in Project Euclid: 18 October 2011

Permanent link to this document
https://projecteuclid.org/euclid.jap/1318940459

Digital Object Identifier
doi:10.1239/jap/1318940459

Mathematical Reviews number (MathSciNet)
MR2865620

Zentralblatt MATH identifier
1229.60075

Subjects
Primary: 60H10: Stochastic ordinary differential equations [See also 34F05]
Secondary: 60G51: Processes with independent increments; Lévy processes 60H35: Computational methods for stochastic equations [See also 65C30] 60K25: Queueing theory [See also 68M20, 90B22]

Keywords
Lévy process queues with many servers storage model stochastic differential equation martingale time change

Citation

Reed, Josh; Zwart, Bert. A piecewise linear stochastic differential equation driven by a Lévy process. J. Appl. Probab. 48A (2011), 109--119. doi:10.1239/jap/1318940459. https://projecteuclid.org/euclid.jap/1318940459


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