Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An approximation of It\^o diffusions based on simple random walks   The aim of this paper is to develop a sequence of discrete approximations to
a one-dimensional It\^o diffusion that almost surely converges to a weak
solution of the given stochastic differential equation. Under suitable
conditions, the solution of the stochastic differential equation can be reduced
to the solution of an ordinary differential equation plus an application of
Girsanov's theorem to adjust the drift. The discrete approximation is based on
a specific strong approximation of Brownian motion by simple, symmetric random
walks (the so-called "twist and shrink" method). A discrete It\^o's formula is
also used during the discrete approximation.

26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph