Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Time inhomogeneous Stochastic Differential Equations involving the local
  time of the unknown process, and associated parabolic operators   In this paper we study time-inhomogeneous versions of one-dimensional
Stochastic Differential Equations (SDE) involving the Local Time of the unknown
process on curves. After proving existence and uniqueness for these SDE under
mild assumptions, we explore their link with Parabolic Differential Equations
(PDE) with transmission conditions. We study the regularity of solutions of
such PDE and ensure the validity of a Feynman-Kac representation formula. These
results are then used to characterize the solutions of these SDE as
time-inhomogeneous Markov Feller processes.

3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
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The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
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The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int