The Annals of Applied Probability

A generalized backward scheme for solving nonmonotonic stochastic recursions

P. Moyal

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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.

Article information

Source
Ann. Appl. Probab. Volume 25, Number 2 (2015), 582-599.

Dates
First available in Project Euclid: 19 February 2015

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1424355124

Digital Object Identifier
doi:10.1214/14-AAP1004

Mathematical Reviews number (MathSciNet)
MR3313749

Zentralblatt MATH identifier
1318.60038

Subjects
Primary: 60G10: Stationary processes 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 60K25: Queueing theory [See also 68M20, 90B22] 37H99: None of the above, but in this section

Keywords
Stochastic recursions stationary solutions enriched probability space ergodic theory queuing theory

Citation

Moyal, P. A generalized backward scheme for solving nonmonotonic stochastic recursions. Ann. Appl. Probab. 25 (2015), no. 2, 582--599. doi:10.1214/14-AAP1004. https://projecteuclid.org/euclid.aoap/1424355124


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