Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Well-posedness and numerical schemes for one-dimensional McKean-Vlasov
  equations and interacting particle systems with discontinuous drift   In this paper, we first establish well-posedness results for one-dimensional
McKean-Vlasov stochastic differential equations (SDEs) and related particle
systems with a measure-dependent drift coefficient that is discontinuous in the
spatial component, and a diffusion coefficient which is a Lipschitz function of
the state only. We only require a fairly mild condition on the diffusion
coefficient, namely to be non-zero in a point of discontinuity of the drift,
while we need to impose certain structural assumptions on the
measure-dependence of the drift. Second, we study Euler-Maruyama type schemes
for the particle system to approximate the solution of the one-dimensional
McKean-Vlasov SDE. Here, we will prove strong convergence results in terms of
the number of time-steps and number of particles. Due to the discontinuity of
the drift, the convergence analysis is non-standard and the usual strong
convergence order $1/2$ known for the Lipschitz case cannot be recovered for
all schemes.

9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org