# BSDEs with no driving martingale, Markov processes and  associated Pseudo Partial Differential Equations. Part II: Decoupled mild solutions and Examples.

Abstract : Let  $(\mathbb{P}^{s,x})_{(s,x)\in[0,T]\times E}$ be a family of probability measures,  where $E$ is a Polish space, defined on the canonical probability space ${\mathbb D}([0,T],E)$ 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 {\it Pseudo-PDE} % with generator $a$  for which we introduce a notion of so called {\it 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.
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https://hal.archives-ouvertes.fr/hal-01505974
Contributor : Francesco Russo <>
Submitted on : Wednesday, April 12, 2017 - 8:12:24 AM
Last modification on : Wednesday, January 23, 2019 - 10:29:31 AM
Document(s) archivé(s) le : Thursday, July 13, 2017 - 12:12:31 PM

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

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Adrien Barrasso, Francesco Russo. BSDEs with no driving martingale, Markov processes and  associated Pseudo Partial Differential Equations. Part II: Decoupled mild solutions and Examples.. 2017. 〈hal-01505974〉

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