Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A maximum principle for Markov-modulated SDEs of mean-field type and
  mean-field game   In this paper, we analyze mean-field game modulated by finite states markov
chains. We first develop a sufficient stochastic maximum principle for the
optimal control of a Markov-modulated stochastic differential equation (SDE) of
mean-field type whose coefficients depend on the state of the process, some
functional of its law as well as variation of time and sample. As coefficients
are perturbed by a Markov chain and thus random, to study such SDEs, we analyze
existence and uniqueness of solutions of a class of mean-field type SDEs whose
coefficients are random Lipschitz as well as the property of propagation of
chaos for associated interacting particles system with method parallel to
existing results as a byproduct. We also solve approximate Nash equilibrium for
the Markov-modulated mean-field game by mean-field theory.

9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th