A simple procedure is proposed for estimating the coefficients {[psi]} from observations of the linear process X1=[summation operator]xJ=0[psi]JZ1-j, 1=1,2... The method is based on the representation of X1 in terms of the innovations, Xn-Xn, N=1,..., 1, where Xn is the best mean square...

A system is subject to random failure with failure rate k(Xt) dependent upon the level Xt of accumulated damage at time t. Given the replacement cost C and the additional cost K for replacement after failure, an optimum level of damage at which replacement should be made is investigated when the...

In order to predict unobserved values of a linear process with infinite variance, we introduce a linear predictor which minimizes the dispersion (suitably defined) of the error distribution. When the linear process is driven by symmetric stable white noise this predictor minimizes the scale...

Necessary and sufficient conditions for the existence of a strictly stationary solution of the equations defining a general Lévy-driven continuous-parameter ARMA process with index set are determined. Under these conditions the solution is shown to be unique and an explicit expression is given...