DECAY AND GROWTH RATES OF SOLUTIONS OF SCALAR STOCHASTIC DELAY DIFFERENTIAL EQUATIONS WITH UNBOUNDED DELAY AND STATE DEPENDENT NOISE

DOI10.1142/S0219493705001353zbMath1078.34059MaRDI QIDQ5694400

John A. D. Appleby

Publication date: 30 September 2005

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

zbMATH Keywords

exponential stabilityasymptotic behaviour

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Stochastic functional-differential equations (34K50) Growth, boundedness, comparison of solutions to functional-differential equations (34K12)

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Cites Work

• Asymptotic representation of solutions of the equation \(\dot y(t)=\beta(t)[y(t)-y(t-\tau(t))\)]
• Non-exponential stability of scalar stochastic Volterra equations.
• The stable manifold theorem for non-linear stochastic systems with memory. II: The local stable manifold theorem.
• Equations with unbounded delay: a survey
• The functional-differential equation $y'\left( x \right) = ay\left( {\lambda x} \right) + by\left( x \right)$