Elliptic PDEs with distributional drift and backward SDEs driven by a càdlàg martingale with random terminal time
august, 2017
Publication type:
Paper in peer-reviewed journals
Journal:
Stochastics and Dynamics., vol. 17, pp. 1750030
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Keywords :
Backward stochastic differential equations;
random terminal time; martingale problem; distributional drift; elliptic partial differential equations.
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.
BibTeX:
@article{Rus-Wur-2017, author={Francesco Russo and Lukas Wurzer }, title={Elliptic PDEs with distributional drift and backward SDEs driven by a càdlàg martingale with random terminal time }, doi={10.1142/S0219493717500307 }, journal={Stochastics and Dynamics. }, year={2017 }, month={8}, volume={17 }, pages={1750030}, }