Comparison and converse comparison theorems for backward stochastic differential equations with Markov chain noise

2014/04/08 by Zhe Yang, Yang, Zhe, Dimbinirina Ramarimbahoaka +3 · 1 citation
Economics, Econometrics and Finance · Engineering · Mathematics · #FOS: Mathematics #Mathematical Biology Tumor Growth #Probability (math.PR) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1404.2213

openalex publication_date 2014/04/08 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

Comparison and converse comparison theorems are important parts of the research on backward stochastic differential equations. In this paper, we obtain comparison results for one dimensional backward stochastic differential equations with Markov chain noise, extending and generalizing previous work under natural and simplified hypotheses, and establish a converse comparison theorem for the same type of equation after giving the definition and properties of a type of nonlinear expectation: f-expectation.

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• Stochastic control for Backward Stochastic Differential Equations with semi-Markov chain noises

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