Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weak variable step-size Euler schemes for stochastic differential
  equations based on controlling conditional moments   We address the weak numerical solution of stochastic differential equations
driven by independent Brownian motions (SDEs for short). This paper develops a
new methodology to design adaptive strategies for determining automatically the
step-sizes of the numerical schemes that compute the mean values of smooth
functions of the solutions of SDEs. First, we introduce a general method for
constructing variable step-size weak schemes for SDEs, which is based on
controlling the matching between the first conditional moments of the
increments of the numerical integrator and the ones corresponding to an
additional weak approximation. To this end, we use certain local discrepancy
functions that do not involve sampling random variables. Precise directions for
designing suitable discrepancy functions and for selecting starting step-sizes
are given. Second, we introduce three variable step-size Euler schemes derived
from three different discrepancy functions, as well as four variable step-size
higher order weak schemes are proposed. Third, to compute the expectation of
functionals of diffusion processes a general procedure for designing adaptive
schemes with variable step-size and sample-size is presented, which combines a
conventional Monte Carlo technique for estimating the total number of
simulations with the new variable step-size weak schemes. Finally, a variety of
numerical simulations are presented to show the potential of the introduced
variable step-size strategies and adaptive schemes to overcome known
instability problems of the conventional fixed step-size schemes in the
computation of diffusion functional expectations.

7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc