Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
Non-exponential Stability of Scalar Stochastic Volterra Equations
 

Summary: Non-exponential Stability of Scalar Stochastic
Volterra Equations
John A. D. Appleby 1
School of Mathematical Sciences, Dublin City University, Dublin 9, Ireland.
David W. Reynolds 2
School of Mathematical Sciences, Dublin City University, Dublin 9, Ireland.
Abstract
We study convergence rates to zero of solutions of the scalar equation
dX(t) = f(X(t)) +
t
0
k(t - s)g(X(s)) ds dt + h(X(t)) dB(t),
where f, g, h are globally Lipschitz, xg(x) > 0 for non-zero x, and k is continuous,
integrable, positive and limt k(t - s)/k(t) = 1, for s > 0. Then
lim sup
t
|X(t)|
k(t)
= a.e. on A,
for nontrivial solutions satisfying limt X(t) = 0 on A, a set of positive probability.

  

Source: Appleby, John - School of Mathematical Sciences, Dublin City University

 

Collections: Mathematics