On a class of Markov BSDEs with generalized driver

Elena Issoglio (1) , Francesco Russo (2)

1 School of Mathematics [Leeds]
2 UMA - Unité de Mathématiques Appliquées

We are concerned with BSDEs where the driver contains a distributional term (in the sense of generalised functions). We introduce an integral operator to give sense to the equation and then we show the existence of a strong solution. Because of the irregularity of the driver, the Y-component of a couple (Y, Z) solving the BSDE is not necessarily a semimartingale but a weak Dirichlet process.

Mots clés: Backward stochastic differential equations (BSDEs); distributional driver; weak Dirichlet process; pointwise product; generalised and rough coefficients

Domaines: Probabilités [math.PR]

Elena Issoglio, Francesco Russo. On a class of Markov BSDEs with generalized driver. 2018. ⟨hal-01786119v1⟩