Backward Stochastic Differential Equations with no driving martingale, Markov processes and associated Pseudo Partial Differential Equations.

march, 2022
Publication type:
Paper in peer-reviewed journals
Journal:
Journal of Stochastic Analysis (JOSA)., vol. 3, Nr. 1
arXiv:
assets/images/icons/icon_arxiv.png 1701.02899
Keywords :
Martingale problem; pseudo-PDE; Markov processes; backward stochastic differential equation.
Abstract:
We discuss a class of Backward Stochastic Differential Equations (BSDEs) with no driving martingale. When the randomness of the driver depends on a general Markov process $X$, those BSDEs are denominated Markovian BSDEs and can be associated to a deterministic problem, called Pseudo-PDE which constitute the natural generalization of a parabolic semilinear PDE which naturally appears when the underlying filtration is Brownian. We consider two aspects of well-posedness for the Pseudo-PDEs: {\it classical} and {\it martingale} solutions.
BibTeX:
@article{Bar-Rus-2022-1,
    author={Adrien Barrasso and Francesco Russo },
    title={Backward Stochastic Differential Equations with no driving 
           martingale, Markov processes and associated Pseudo Partial 
           Differential Equations. },
    journal={Journal of Stochastic Analysis (JOSA). },
    year={2022 },
    month={3},
    volume={3, Nr. 1 },
}