Ergodic backward stochastic difference equations. Issue 8 (16th November 2016)

• Record Type: Journal Article
• Authors: Allan, Andrew L.; Cohen, Samuel N.
• Is Part Of: Stochastics. Volume 88:Issue 8(2016)
• Page Start: 1207
• Page End: 1239
• Publication Date: 2016-11-16
• Subjects: Ergodic BSDE -- Markov chain -- uniform ergodicity -- Nummelin splitting -- ergodic control; 60J10 -- 93E20 -- 60F99; Stochastic processes -- Periodicals; Probabilities -- Periodicals; 519.2
• DOI: 10.1080/17442508.2016.1224881
• Languages: English
• ISSNs: 1744-2508

Abstract

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.