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Ergodic backward stochastic difference equations

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.
Publication status:
Published
Peer review status:
Peer reviewed
Version:
Accepted Manuscript

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Publisher copy:
10.1080/17442508.2016.1224881

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Department:
Wadham College
Publisher:
Taylor & Francis Publisher's website
Journal:
Stochastics Journal website
Volume:
88
Issue:
8
Pages:
1207–1239
Publication date:
2016-09-02
Acceptance date:
2016-08-05
DOI:
EISSN:
1744-2516
ISSN:
0090-9491
Pubs id:
pubs:638038
URN:
uri:fb51f156-81c3-4d15-b303-aac47ccc7598
UUID:
fb51f156-81c3-4d15-b303-aac47ccc7598
Local pid:
pubs:638038

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