We investigate stochastic Volterra equations and their limiting laws. The we consider are driven by a Hilbert space valued \Levy noise integration kernels may have non-linear dependence on the current state of process. Our method is based an embedding into functions which allows to represent solution equation as boundary value partial differential equation. first gather abstract results give mo...

We study the nonlinear wave equation utt ? c 2 uxx = (u) u(0; t) = 0 = u(; t) (0.1) with an analytic nonlinearity of the type (u) = u 3 + P k4 k u k. On each small{energy surface we consider a solution of the linearized system with initial datum having the proole of an elliptic sinus: we show that solutions starting close to the corresponding phase space trajectory remain close to it for times ...

Yearly electricity consumption trends of most developing countries usually exhibit approximately exponential growth curves. An optimized nonhomogeneous exponential model (ONEM) is proposed as a method of forecasting electricity consumption by using trend extrapolation. The parameters of the nonhomogeneous exponential equation are obtained by using the inverse accumulated generating operation, d...