Ergodic Backward Stochastic Difference Equations
Probability
2015-09-02 v1 Optimization and Control
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.
Cite
@article{arxiv.1509.00231,
title = {Ergodic Backward Stochastic Difference Equations},
author = {Andrew L. Allan and Samuel N. Cohen},
journal= {arXiv preprint arXiv:1509.00231},
year = {2015}
}