Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Strong convergence of the symmetrized Milstein scheme for some CEV-like
  SDEs   In this paper we study the rate of convergence of a symmetrized version of
the Milstein scheme applied to the solution of the one dimensional SDE $$X_t =
x_0 + \int_{0}^t{b(X_s)ds}+\int_{0}^t{\sigma |X_s|^\alpha dW_s},
\;x_0>0,\;\sigma>0,\; \alpha\in[\tfrac{1}{2},1).$$ Assuming $b(0)/\sigma^2$ big
enough, and $b$ smooth, we prove a strong rate of convergence of order one,
recovering the classical result of Milstein for SDEs with smooth diffusion
coefficient. In contrast with other recent results, our proof does not relies
on Lamperti transformation, and it can be applied to a wide class of drift
functions. On the downside, our hypothesis on the critical parameter value
$b(0)/\sigma^2$ is more restrictive than others available in the literature.
Some numerical experiments and comparison with various other schemes complement
our theoretical analysis that also applies for the simple projected Milstein
scheme with same convergence rate.

9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph