Open Access
2016 Stability and Markov property of forward backward minimal supersolutions
Samuel Drapeau, Christoph Mainberger
Electron. J. Probab. 21: 1-15 (2016). DOI: 10.1214/16-EJP4276


We show stability and locality of the minimal supersolution of a forward backward stochastic differential equation with respect to the underlying forward process under weak assumptions on the generator. The forward process appears both in the generator and the terminal condition. Painlevé-Kuratowski and Convex Epi-convergence are used to establish the stability. For Markovian forward processes the minimal supersolution is shown to have the Markov property. Furthermore, it is related to a time-shifted problem and identified as the unique minimal viscosity supersolution of a corresponding PDE.


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Samuel Drapeau. Christoph Mainberger. "Stability and Markov property of forward backward minimal supersolutions." Electron. J. Probab. 21 1 - 15, 2016.


Received: 30 April 2015; Accepted: 17 May 2016; Published: 2016
First available in Project Euclid: 17 June 2016

zbMATH: 1345.60049
MathSciNet: MR3515571
Digital Object Identifier: 10.1214/16-EJP4276

Primary: 35D40 , 60H10 , 60H30

Keywords: FBSDEs , Markov property , stability , Supersolutions of backward stochastic differential equations , viscosity supersolutions

Vol.21 • 2016
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