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April 2015 A generalized backward scheme for solving nonmonotonic stochastic recursions
P. Moyal
Ann. Appl. Probab. 25(2): 582-599 (April 2015). DOI: 10.1214/14-AAP1004

Abstract

We propose an explicit construction of a stationary solution for a stochastic recursion of the form $X\circ\theta=\varphi(X)$ on a partially-ordered Polish space, when the monotonicity of $\varphi$ is not assumed. Under certain conditions, we show that an extension of the original probability space exists, on which a solution is well defined, and construct explicitly this extension using a randomized contraction technique. We then provide conditions for the existence of a solution on the original space. We finally apply these results to the stability study of two nonmonotonic queuing systems.

Citation

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P. Moyal. "A generalized backward scheme for solving nonmonotonic stochastic recursions." Ann. Appl. Probab. 25 (2) 582 - 599, April 2015. https://doi.org/10.1214/14-AAP1004

Information

Published: April 2015
First available in Project Euclid: 19 February 2015

zbMATH: 1318.60038
MathSciNet: MR3313749
Digital Object Identifier: 10.1214/14-AAP1004

Subjects:
Primary: 60G10, 60J10
Secondary: 37H99, 60K25

Rights: Copyright © 2015 Institute of Mathematical Statistics

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Vol.25 • No. 2 • April 2015
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