Stability and Markov property of forward backward minimal supersolutions
Copyright policy )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. Painlev��-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.
- Humboldt-Universität zu Berlin Germany
- Shanghai Jiao Tong University China (People's Republic of)
- Technical University of Berlin Germany
- TECHNISCHE UNIVERSITAT BERLIN Germany
- Technical University of Berlin Germany
35D40, Probability (math.PR), Markov property, supersolutions of backward stochastic differential equations, Applications of stochastic analysis (to PDEs, etc.), stability, Stochastic ordinary differential equations (aspects of stochastic analysis), Viscosity solutions to PDEs, supersolutions, Mathematics - Analysis of PDEs, forward-backward stochastic differential equations, FBSDEs, FOS: Mathematics, Continuous-time Markov processes on general state spaces, viscosity supersolutions, 60H10, 60H30, Mathematics - Probability, Analysis of PDEs (math.AP)
35D40, Probability (math.PR), Markov property, supersolutions of backward stochastic differential equations, Applications of stochastic analysis (to PDEs, etc.), stability, Stochastic ordinary differential equations (aspects of stochastic analysis), Viscosity solutions to PDEs, supersolutions, Mathematics - Analysis of PDEs, forward-backward stochastic differential equations, FBSDEs, FOS: Mathematics, Continuous-time Markov processes on general state spaces, viscosity supersolutions, 60H10, 60H30, Mathematics - Probability, Analysis of PDEs (math.AP)
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