Invariance and Monotonicity for Stochastic Delay Differential Equations

2012/01/05 by Igor Chueshov, Chueshov, Igor, Michael Scheutzow +1
Mathematics · #34K50 #37H10 #60H10 #93E15 #Dynamical Systems (math.DS) #FOS: Mathematics #Probability (math.PR) #math.DS #math.PR #msc:34K50 #msc:37H10 #msc:60H10 #msc:93E15

paper · pdf · doi:10.48550/arxiv.1201.1226

27 pages

arxiv created 2012/01/05 · arxiv updated 2012/01/06

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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