The stochastic delay differential equationis considered, where Z(t) is a process with independent stationary increments and a is a finite signed measure. We obtain necessary and sufficient conditions for the existence of a stationary solution to this equation in terms of a and the Lévy measure...

The geometric Brownian motion is the solution of a linear stochastic differential equation in the Itô sense. If one adds to the drift term a possible nonlinear time-delayed term and starts with a non-negative initial process then the process generated in this way, may hit zero and may oscillate...

This paper presents a general theory that works out the relation between coherent risk measures, valuation bounds, and certain classes of portfolio optimization problems. It is economically general in the sense that it works for any cash stream spaces, be it in dynamic trading settings, one-step...

Assume L is a non-deterministic real valued Lévy process and f is a smooth function on [0,t]

Multivariate versions of the law of large numbers and the central limit theorem for martingales are given in a generality that is often necessary when studying statistical inference for stochastic process models. To illustrate the usefulness of the results, we consider estimation for a...

We obtain an explicit form of fine large deviation theorems for the log-likelihood ratio in testing models with observed Ornstein-Uhlenbeck processes and get explicit rates of decrease for error probabilities of Neyman-Pearson, Bayes, and minimax tests. We also give expressions for the rates of...

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....