Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convergence and stability of two classes of theta-Milstein schemes for
  stochastic differential equations   This paper examines convergence and stability of the two classes of
theta-Milstein schemes for stochastic differential equations (SDEs) with
non-global Lipschitz continuous coefficients: the split-step theta-Milstein
(SSTM) scheme and the stochastic theta-Milstein (STM) scheme. For
\theta\in[1/2,1], this paper concludes that the two classes of theta-Milstein
schemes converge strongly to the exact solution with the order 1. For \theta
\in [0,1/2], under the additional linear growth condition for the drift
coefficient, these two classes of the theta-Milstein schemes are also strongly
convergent with the standard order. This paper also investigates exponential
mean-square stability of these two classes of the theta-Milstein schemes. For
\theta\in(1/2, 1], these two theta-Milstein schemes can share the exponential
mean-square stability of the exact solution. For \theta\in[0, 1/2], similar to
the convergence, under the additional linear growth condition, these two
theta-Milstein schemes can also reproduce the exponential mean-square stability
of the exact solution.

25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin