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Almost sure subexponential decay rates of scalar Ito-Volterra equations.

Appleby, John A.D. (2004) Almost sure subexponential decay rates of scalar Ito-Volterra equations. In: 7th Colloquim on the Qualitative Theory of Differential Equations, 14-18 July, 2003, Szeged, Hungary.

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Abstract

The paper studies the subexponential convergence of solutions of scalar Itˆo-Volterra equations. First, we consider linear equations with an instantaneous multiplicative noise term with intensity . If the kernel obeys lim t!1 k0(t)/k(t) = 0, and another nonexponential decay criterion, and the solution X tends to zero as t ! 1, then limsup t!1 log |X(t)| log(tk(t)) = 1 − (||), a.s. where the random variable (||) ! 0 as ! 1 a.s. We also prove a decay result for equations with a superlinear diffusion coefficient at zero. If the deterministic equation has solution which is uniformly asymptotically stable, and the kernel is subexponential, the decay rate of the stochastic problem is exactly the same as that of the underlying deterministic problem.

Item Type:Conference or Workshop Item (Paper)
Event Type:Conference
Refereed:Yes
Uncontrolled Keywords:almost sure exponential asymptotic stability; Itˆo- Volterra equations;
Subjects:Mathematics > Stochastic analysis
DCU Faculties and Centres:DCU Faculties and Schools > Faculty of Science and Health > School of Mathematical Sciences
Official URL:http://www.math.u-szeged.hu/ejqtde/
Use License:This item is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 3.0 License. View License
ID Code:12
Deposited On:26 Oct 2006 by DORAS Administrator. Last Modified 29 Jan 2009 16:30

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