Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Numerical methods for mean-field stochastic differential equations with
  jumps   In this paper, we are devoted to the numerical methods for mean-field
stochastic differential equations with jumps (MSDEJs). First by using the
mean-field It\^o formula [Sun, Yang and Zhao, Numer. Math. Theor. Meth. Appl.,
10 (2017), pp.~798--828], we develop the It\^o formula and construct the
It\^o-Taylor expansion for MSDEJs. Then based on the It\^o-Taylor expansion, we
propose the strong order $\gamma$ and the weak order $\eta$ It\^o-Taylor
schemes for MSDEJs. %We theoretically prove The strong and weak convergence
rates $\gamma$ and $\eta$ of the strong and weak It\^o-Taylor schemes are
theoretically proved, respectively. Finally some numerical tests are also
presented to verify our theoretical conclusions.

29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con