Almost Sure Asymptotic Stability of Stochastic Volterra Integro-Differential Equations with Fading Perturbations

TY - JOUR

T1 - Almost Sure Asymptotic Stability of Stochastic Volterra Integro-Differential Equations with Fading Perturbations

AU - Appleby, John

AU - Riedle, Markus

PY - 2006

Y1 - 2006

N2 - In this note, we address the question of how large a stochastic perturbation an asymptotically stable linear functional differential system can tolerate without losing the property of being pathwise asymptotically stable. In particular, we investigate noise perturbations that are either independent of the state or influenced by the current and past states. For perturbations independent of the state, we prove that the assumed rate of fading for the noise is optimal.

AB - In this note, we address the question of how large a stochastic perturbation an asymptotically stable linear functional differential system can tolerate without losing the property of being pathwise asymptotically stable. In particular, we investigate noise perturbations that are either independent of the state or influenced by the current and past states. For perturbations independent of the state, we prove that the assumed rate of fading for the noise is optimal.

KW - Almost sure asymptotic stability

KW - Exponential asymptotic stability

KW - Itô-Volterra equations

KW - Simulated annealing

KW - Stochastic delay differential equations

KW - Stochastic functional differential equations

KW - Uniform asymptotic stability

U2 - 10.1080/07362990600753536

DO - 10.1080/07362990600753536

M3 - Article

SN - 0736-2994

VL - 24

SP - 813

EP - 826

JO - STOCHASTIC ANALYSIS AND APPLICATIONS

JF - STOCHASTIC ANALYSIS AND APPLICATIONS

IS - 4

ER -