In this paper we study asymptotic behaviour of marked point processes describing failure processes of repairable systems in which repair decisions depend on the past. Under natural conditions on system parameters such processes admit unique time stationary distributions and are ergodic....

Based on recent results on the exploitation of "drift criteria" for general state-space Markov processes, we derive rates of convergence for (moments of ) processes associated with a renewal process with common inter-renewal time distribution F. Some of the results are classical and some are...

We propose two general methods for coupling marked point processes (MPPs) on the real half-line that are explicitly formulated in terms of (canonical) compensators. These couplings are related to several results in the literature as compensator bounds for the total variation distance between two...

We consider the path Zt described by a standard Brownian motion in on some time interval [0,t]. This is a random compact subset of . Using the support (curvature) measures of [D. Hug, G. Last, W. Weil, A local Steiner-type formula for general closed sets and applications, Math. Z. 246...

Starting with a basic lemma on conditional distributions we give a unified approach to some results for point processes that are based on disintegration of suitable Campbell measures. In particular, we discuss consistency relations in terms of the (conditional) Palm measures, the (canonical and...

We consider markings and thinnings of a marked point process on the real half-line and derive conditions which allow to compute their (internal) compensators in terms of the compensator of the original point process and certain stochastic kernels describing conditional mark distributions. As...

We consider two marked point processes [Phi] and [Psi] on the real half-line such that [Psi] is an -predictable thinning and marking of [Phi]. Using the method of the probability of reference we derive linear and non-linear filtering equations for the conditional distribution , where {gt} is a...