Der Begriff der A-Stabilität wird auf lineare Differentialgleichungen mit Gedächtnis übertragen. Es erfolgt eine explizite Berechnung des Stabilitätsgebietes des expliziten Eulerverfahrens für affine Testgleichungen mit einem reellen Parameter und einer echten Zeitverzögerung im Driftterm....

The paper considers the derivation of weak discrete time approximations for solutions of stochastic differential equations with time delay. These are suitable for Monte Carlo simulation and allow the computation of expectations for functionals of stochastic delay equations. The suggested...

Numerical solutions of SDDE often reflect to only a limited extent the exact solution behaviour. Hence it is necessary to identify those parameters of SDDE and algorithm for which a numerical method in use is reliable. For affine SDDE test equations, there exist estimates of the stability...

In this paper the asymptotic behaviour of the maximum likelihood and Bayesian estimators of a delay parameter is studied. The observed process is supposed to be the solution of a linear stochastic differential equation with one time delay term. It is shown that these estimators are consistent...