Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Invariance and Monotonicity for Stochastic Delay Differential Equations   We study invariance and monotonicity properties of Kunita-type stochastic
differential equations in $\RR^d$ with delay. Our first result provides
sufficient conditions for the invariance of closed subsets of $\RR^d$. Then we
present a comparison principle and show that under appropriate conditions the
stochastic delay system considered generates a monotone (order-preserving)
random dynamical system. Several applications are considered.

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The categories of this paper are: nlin
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
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The categories of this paper are: cmp-lg
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The categories of this paper are: alg-geom
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The categories of this paper are: astro-ph
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The categories of this paper are: supr-con
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The categories of this paper are: q-bio