Stability theory for Volterra equations

Boundedness and stability of discrete Volterra equations

Duality Theory in Filtering Problem for Discrete Volterra Equations

The ltering problem for discrete Volterra equations is a nontrivial task due to an increasing dimension of the equivalent single step process model A di erence equation of a moderate dimension is chosen as an approximate model for the original system Then the reduced Kalman lter can be used as an approximate but e cient estimator Using the duality theory of convex variational problems a level o...

Stability of a system of Volterra integro-differential equations

Using new and known forms of Lyapunov functionals, this paper proposes new stability criteria for a system of Volterra integro-differential equations.  2003 Elsevier Science (USA). All rights reserved.

Stability and Asymptoticity of Volterra Difference Equations: A Progress Report

We survey some of the fundamental results on the stability and asymptoticity of linear Volterra difference equations. The method of Z-transform is heavily utilized in equations of convolution type. An example is given to show that uniform asymptotic stability does not necessarily imply exponential stabilty. It is shown that the two notions are equivalent if the kernel decays exponentially. For ...

Stochastic Volterra integro-differential equations: stability and numerical methods

We consider the reliability of some numerical methods in preserving the stability properties of the linear stochastic functional differential equation ẋ(t) = αx(t) + β ∫ t 0 x(s)ds+ σx(t− τ )Ẇ (t), where α, β, σ, τ ≥ 0 are real constants, and W (t) is a standard Wiener process. We adopt the shorthand notation of ẋ(t) to represent the differential dx(t) etc. Our choice of test equation is a stoc...