EXPONENTIAL GROWTH RATES FOR STOCHASTIC DELAY DIFFERENTIAL EQUATIONS

DOI10.1142/S0219493705001468zbMath1079.60058OpenAlexW2153620920MaRDI QIDQ5694402

Michael K. R. Scheutzow

Publication date: 30 September 2005

Published in: Stochastics and Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219493705001468

zbMATH Keywords

Lyapunov functionalstochastic delay equationLyapunov exponent

Mathematics Subject Classification ID

Continuous-time Markov processes on general state spaces (60J25) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Stochastic functional-differential equations (34K50) Random dynamical systems aspects of multiplicative ergodic theory, Lyapunov exponents (37H15) Stochastic integral equations (60H20)

Related Items (10)

Stochastic functional differential equations with infinite delay under non-Lipschitz coefficients: existence and uniqueness, Markov property, ergodicity, and asymptotic log-Harnack inequality ⋮ Asymptotic Bismut formulae for stochastic functional differential equations with infinite delay ⋮ Stability of stochastic functional differential equations with random switching and applications ⋮ Generalized couplings and ergodic rates for SPDEs and other Markov models ⋮ Almost sure exponential stability of hybrid stochastic functional differential equations ⋮ Almost sure exponential stability and stabilization of hybrid stochastic functional differential equations with Lévy noise ⋮ Subgeometric rates of convergence of Markov processes in the Wasserstein metric ⋮ Almost Sure Exponential Stability of Stochastic Differential Delay Equations ⋮ Asymptotic coupling and a general form of Harris' theorem with applications to stochastic delay equations ⋮ Stability of stochastic functional differential equations with regime-switching: analysis using Dupire's functional Itô formula

Cites Work

• The stable manifold theorem for non-linear stochastic systems with memory. I: Existence of the semiflow.
• The stable manifold theorem for non-linear stochastic systems with memory. II: The local stable manifold theorem.
• Qualitative behaviour of stochastic delay equations with a bounded memory
• Nonlinear flows of stochastic linear delay equations
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