Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Invariant measures and Euler-Maruyama's approximations of
  state-dependent regime-switching diffusions   Regime-switching processes contain two components: continuous component and
discrete component, which can be used to describe a continuous dynamical system
in a random environment. Such processes have many different properties than
general diffusion processes, and much more difficulties are needed to be
overcome due to the intensive interaction between continuous and discrete
component. We give conditions for the existence and uniqueness of invariant
measures for state-dependent regime-switching diffusion processes by
constructing a new Markov chain to control the evolution of the state-dependent
switching process. We also establish the strong convergence in the $L^1$-norm
of the Euler-Maruyama's approximation and estimate the order of error. A
refined application of Skorokhod's representation of jumping processes plays a
substantial role in this work.

33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an