Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Full history recursive multilevel Picard approximations for ordinary
  differential equations with expectations   We consider ordinary differential equations (ODEs) which involve expectations
of a random variable. These ODEs are special cases of McKean-Vlasov stochastic
differential equations (SDEs). A plain vanilla Monte Carlo approximation method
for such ODEs requires a computational cost of order $\varepsilon^{-3}$ to
achieve a root-mean-square error of size $\varepsilon$. In this work we adapt
recently introduced full history recursive multilevel Picard (MLP) algorithms
to reduce this computational complexity. Our main result shows for every
$\delta>0$ that the proposed MLP approximation algorithm requires only a
computational effort of order $\varepsilon^{-(2+\delta)}$ to achieve a
root-mean-square error of size $\varepsilon$.

21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom