Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rate of convergence for numerical solutions to SFDEs with jumps   In this paper, we are interested in the numerical solutions of stochastic
functional differential equations (SFDEs) with {\it jumps}. Under the global
Lipschitz condition, we show that the $p$th moment convergence of the
Euler-Maruyama (EM) numerical solutions to SFDEs with jumps has order $1/p$ for
any $p\ge 2$. This is significantly different from the case of SFDEs without
jumps where the order is 1/2 for any $p\ge 2$. It is therefore best to use the
mean-square convergence for SFDEs with jumps. Consequently, under the local
Lipschitz condition, we reveal that the order of the mean-square convergence is
close to 1/2, provided that the local Lipschitz constants, valid on balls of
radius $j$, do not grow faster than $\log j$.

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The categories of this paper are: gr-qc
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The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: nlin
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The categories of this paper are: bayes-an
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The categories of this paper are: physics
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The categories of this paper are: adap-org
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The categories of this paper are: hep-th
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The categories of this paper are: q-fin