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

may, 2021
Type de publication :
Article (revues avec comité de lecture)
Journal :
Journal of Theoretical Probabililty.
HAL :
hal-01505974
arXiv :
assets/images/icons/icon_arxiv.png 1704.03650
Mots clés :
Martingale problem; pseudo-PDE; Markov processes; backward stochastic differential equation; decoupled mild solutions.
Résumé :
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 ${\mathbbm D}([0,T],E)$
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. 


BibTeX :
@article{Bar-Rus-2021-1,
    author={Adrien Barrasso and Francesco Russo },
    title={Backward Stochastic Differential Equations with no driving 
           martingale, Markov processes and associated Pseudo Partial 
           Differential Equations. Part II: Decoupled mild solutions and 
           Examples. },
    doi={10.1007/s10959-021-01092-7 },
    journal={Journal of Theoretical Probabililty. },
    year={2021 },
    month={5},
}