Electronic Journal of Probability

Stability and Markov property of forward backward minimal supersolutions

Samuel Drapeau and Christoph Mainberger

Full-text: Open access

Abstract

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.

Article information

Source
Electron. J. Probab., Volume 21 (2016), paper no. 41, 15 pp.

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1466166072

Digital Object Identifier
doi:10.1214/16-EJP4276

Mathematical Reviews number (MathSciNet)
MR3515571

Zentralblatt MATH identifier
1345.60049

Subjects
Primary: 60H10: Stochastic ordinary differential equations [See also 34F05] 60H30: Applications of stochastic analysis (to PDE, etc.) 35D40: Viscosity solutions

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

Rights
Creative Commons Attribution 4.0 International License.

Citation

Drapeau, Samuel; Mainberger, Christoph. Stability and Markov property of forward backward minimal supersolutions. Electron. J. Probab. 21 (2016), paper no. 41, 15 pp. doi:10.1214/16-EJP4276. https://projecteuclid.org/euclid.ejp/1466166072


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