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Ergodic Backward Stochastic Difference Equations

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Type
Preprint
Publication Date
Submission Date
Identifiers
arXiv ID: 1509.00231
Source
arXiv
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Abstract

We consider ergodic backward stochastic differential equations in a discrete time setting, where noise is generated by a finite state Markov chain. We show existence and uniqueness of solutions, along with a comparison theorem. To obtain this result, we use a Nummelin splitting argument to obtain ergodicity estimates for a discrete time Markov chain which hold uniformly under suitable perturbations of its transition matrix. We conclude with an application of this theory to a treatment of an ergodic control problem.

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