Showing papers by "Volker Schmidt published in 1990"

Extended and conditional versions of the pasta property

Abstract: Two types of conditions are discussed ensuring the equality between long-run time fractions and long-run event fractions of stochastic processes with embedded point processes. Modifications of this equality statement are considered. In the current literature (see the references below) several lines of investigation can be observed dealing with generalizations of the fact that Poisson Arrivals see time averages (PASTA). Roughly speaking, the methods used for proving such results can be divided into two classes: (i) Martingale techniques are exploited, where the embedded point process is assumed to admit a stochastic intensity. (ii) Conditional intensities are considered, including their local characterization in the sense of Korolyuk, where the existence of these conditional intensities is either assumed a priori or ensured by the existence of a sufficiently rich family of regular subsets of the state space. We discuss these two approaches within the stationary framework. In particular, a general form of the conditional PASTA property is stated.