# Elliptic PDEs with distributional drift and backward SDEs driven by a càdlàg martingale with random terminal time

2 Unit for Engineering Mathematics
Unit for Engineering Mathematics
Abstract : We introduce a generalized notion of semilinear elliptic partial differential equations where the corresponding second order partial differential operator $L$ has a generalized drift. We investigate existence and uniqueness of generalized solutions of class $C^1$. The generator $L$ is associated with a Markov process $X$ which is the solution of a stochastic differential equation with distributional drift. If the semilinear PDE admits boundary conditions, its solution is naturally associated with a backward stochastic differential equation (BSDE) with random terminal time, where the forward process is $X$. Since $X$ is a weak solution of the forward SDE, the BSDE appears naturally to be driven by a martingale. In the paper we also discuss the uniqueness of a BSDE with random terminal time when the driving process is a general càdlàg martingale.
Keywords :
Type de document :
Pré-publication, Document de travail
2015
Domaine :

https://hal.inria.fr/hal-01023176
Contributeur : Francesco Russo <>
Soumis le : mardi 2 juin 2015 - 10:58:39
Dernière modification le : samedi 18 février 2017 - 01:20:04
Document(s) archivé(s) le : mardi 15 septembre 2015 - 09:26:14

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### Identifiants

• HAL Id : hal-01023176, version 2
• ARXIV : 1407.3218

### Citation

Francesco Russo, Lukas Wurzer. Elliptic PDEs with distributional drift and backward SDEs driven by a càdlàg martingale with random terminal time. 2015. 〈hal-01023176v2〉

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