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Non-exponential stability of scalar stochastic Volterra equations

✍ Scribed by John A.D. Appleby; David W. Reynolds

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
227 KB
Volume
62
Category
Article
ISSN
0167-7152

No coin nor oath required. For personal study only.

✦ Synopsis

We study convergence rates to zero of solutions of the scalar equation

where f, g, h are globally Lipschitz, xg(x) ΒΏ 0 for nonzero x, and k is continuous, integrable, positive and lim tβ†’βˆž k(t -s)=k(t) = 1, for s ΒΏ 0. Then

= ∞ a:e: on A for nontrivial solutions satisfying lim tβ†’βˆž X (t) = 0 on A, a set of positive probability.

πŸ“œ SIMILAR VOLUMES

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