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Non-exponential stability of scalar stochastic Volterra equations

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  • Appleby, John A. D.
  • Reynolds, David W.

Abstract

We study convergence rates to zero of solutions of the scalar equationwhere f, g, h are globally Lipschitz, xg(x)>0 for nonzero x, and k is continuous, integrable, positive and limt-->[infinity] k(t-s)/k(t)=1, for s>0. Thenfor nontrivial solutions satisfying limt-->[infinity] X(t)=0 on A, a set of positive probability.

Suggested Citation

  • Appleby, John A. D. & Reynolds, David W., 2003. "Non-exponential stability of scalar stochastic Volterra equations," Statistics & Probability Letters, Elsevier, vol. 62(4), pages 335-343, May.
    • Handle: RePEc:eee:stapro:v:62:y:2003:i:4:p:335-343
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    References listed on IDEAS

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    1. Liu, Kai & Mao, Xuerong, 1998. "Exponential stability of non-linear stochastic evolution equations," Stochastic Processes and their Applications, Elsevier, vol. 78(2), pages 173-193, November.
    2. Mao, Xuerong, 1992. "Polynomial stability for perturbed stochastic differential equations with respect to semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 41(1), pages 101-116, May.
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    Cited by:

    1. Appleby, John A.D. & Patterson, Denis D., 2021. "Growth and fluctuation in perturbed nonlinear Volterra equations," Applied Mathematics and Computation, Elsevier, vol. 396(C).

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