Ergodic backward stochastic difference equations

Allan, Andrew L.; Cohen, Samuel N.

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.

Citation

Allan, A. L., & Cohen, S. N. (2016). Ergodic backward stochastic difference equations. Stochastics: An International Journal of Probability and Stochastic Processes, 88(8), 1207-1239. https://doi.org/10.1080/17442508.2016.1224881

• Journal Article Type: Article
• Acceptance Date: Aug 5, 2016
• Online Publication Date: Sep 2, 2016
• Publication Date: 2016
• Deposit Date: Jan 24, 2023
• Publicly Available Date: Jan 26, 2023
• Journal: Stochastics
• Print ISSN: 1744-2508
• Electronic ISSN: 1744-2516
• Publisher: Taylor and Francis Group
• Peer Reviewed: Peer Reviewed
• Volume: 88
• Issue: 8
• Pages: 1207-1239
• DOI: https://doi.org/10.1080/17442508.2016.1224881