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

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.
Type de document :
Pré-publication, Document de travail
2017
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https://hal.archives-ouvertes.fr/hal-01505974
Contributeur : Francesco Russo <>
Soumis le : mercredi 12 avril 2017 - 08:12:24
Dernière modification le : vendredi 14 avril 2017 - 01:09:16

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  • HAL Id : hal-01505974, version 1
  • ARXIV : 1704.03650

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Adrien Barrasso, Francesco Russo. Decoupled Mild solutions for Pseudo Partial Differential Equations versus Martingale driven forward-backward SDEs. 2017. <hal-01505974>

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