Integro-partial differential equations with singular terminal condition

Alexandre Popier (1)

1 LMM - Laboratoire Manceau de Mathématiques

In this paper, we show that the minimal solution of a backward stochastic differential equation gives a probabilistic representation of the minimal viscosity solution of an integro-partial differential equation both with a singular terminal condition. Singularity means that at the final time, the value of the solution can be equal to infinity. Different types of regularity of this viscosity solution are investigated: Sobolev, Hölder or strong regularity.

Mots clés: Integro-partial differential equations; viscosity solution; backward stochastic differential equation; singular condition

Domaines: Equations aux dérivées partielles [math.AP]; Probabilités [math.PR]

Alexandre Popier. Integro-partial differential equations with singular terminal condition. 2017. ⟨hal-01293775v3⟩