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

Adrien Barrasso (1, 2) , Francesco Russo (2, 3)

1 X - École polytechnique
2 UMA - Unité de Mathématiques Appliquées
3 OC - Optimisation et commande

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: "classical" and "martingale" solutions.

Mots clés: Markov processes; backward stochastic differential equation.; Martingale problem; pseudo-PDE

Domaines: Probabilités [math.PR]

Adrien Barrasso, Francesco Russo. Backward Stochastic Differential Equations with no driving martingale, Markov processes and associated Pseudo Partial Differential Equations. Journal of Stochastic Analysis , 2022, 3 (1), ⟨10.31390/josa.3.1.03⟩. ⟨hal-01431559v3⟩