Decoupled Mild solutions for Pseudo Partial Differential Equations versus Martingale driven forward-backward SDEs

submitted
Publication type:
Paper in peer-reviewed journals
arXiv:
images/icons/icon_arxiv.png 1704.03650
Keywords :
Martingale problem; pseudo-PDE; Markov processes; backward stochastic differential equation; decoupled mild solutions.
Abstract:
Let P^{s,x}, (s,x)∈[0,T ]×E be a family of probability measures, where E is a Polish space, defined on the canonical probability space ([0, T ], E) of E-valued cadlag functions. We suppose that a martingale problem with respect to a time-inhomogeneous generator a is well-posed. We consider also an associated semilinear Pseudo-PDE for which we introduce a notion of so called decoupled mild solution and study the equivalence with the notion of martingale solution introduced in a companion paper. We also investigate well-posedness for decoupled mild solutions and their relations with a special class of BSDEs without driving martingale. The notion of decoupled mild solution is a good candidate to replace the notion of viscosity solution which is not always suitable when the map a is not a PDE operator.
BibTeX:
@article{Bar-Rus-2200,
    author={Adrien Barrasso and Francesco Russo },
    title={Decoupled Mild solutions for Pseudo Partial Differential 
           Equations versus Martingale driven forward-backward SDEs },
    year={submitted },
}