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2016 Comparison and converse comparison theorems for backward stochastic differential equations with Markov chain noise
Zhe Yang, Dimbinirina Ramarimbahoaka, Robert J. Elliott
Electron. Commun. Probab. 21: 1-10 (2016). DOI: 10.1214/16-ECP4102

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, adapting previous results under simplified hypotheses. We introduce a type of nonlinear expectation, the $f$-expectation, which is an interpretation of the solution to a BSDE, and use it to establish a converse comparison theorem for the same type of equations as those in the comparison results.

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Zhe Yang. Dimbinirina Ramarimbahoaka. Robert J. Elliott. "Comparison and converse comparison theorems for backward stochastic differential equations with Markov chain noise." Electron. Commun. Probab. 21 1 - 10, 2016. https://doi.org/10.1214/16-ECP4102

Information

Received: 1 August 2014; Accepted: 12 February 2016; Published: 2016
First available in Project Euclid: 10 March 2016

zbMATH: 1338.60164
MathSciNet: MR3485394
Digital Object Identifier: 10.1214/16-ECP4102

Subjects:
Primary: 60H15

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