Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Elliptic PDEs with distributional drift and backward SDEs driven by a
  c{\`a}dl{\`a}g martingale with random terminal time   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
c{\`a}dl{\`a}g martingale.

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The categories of this paper are: astro-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: stat
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The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ph
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The categories of this paper are: eess
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The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom
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The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
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The categories of this paper are: supr-con
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The categories of this paper are: hep-th