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Invariance and monotonicity for stochastic delay differential equations

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  • We study invariance and monotonicity properties of Kunita-type sto-chastic differential equations in $\mathbb{R}^d$ with delay. Our first result provides sufficient conditions for the invariance of closed subsets of $\mathbb{R}^d$. 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.
    Mathematics Subject Classification: Primary: 34K50, 37H10; Secondary: 37H10.

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