Invariance and Monotonicity for Stochastic Delay Differential Equations

Igor Chueshov; Michael Scheutzow

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arXiv · 1201.1226

Invariance and Monotonicity for Stochastic Delay Differential Equations

Igor Chueshov·Michael Scheutzow

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Abstract

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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Igor Chueshov, Michael Scheutzow. 2012-01-05. Invariance and Monotonicity for Stochastic Delay Differential Equations. https://arxiv.org/abs/1201.1226

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