Electronic Journal of Probability
- Electron. J. Probab.
- Volume 21 (2016), paper no. 41, 15 pp.
Stability and Markov property of forward backward minimal supersolutions
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.
Electron. J. Probab., Volume 21 (2016), paper no. 41, 15 pp.
Received: 30 April 2015
Accepted: 17 May 2016
First available in Project Euclid: 17 June 2016
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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