For risk processes with a general stationary input, a representation formula of ladder height distributions is proved which includes some additional information on process behaviour at the ladder epoch. The proof is short and probabilistic, and utilizes time reversal, occupation measures and...

The aim of the present paper is to discuss three types of coincidence properties (EPSTA, CEPSTA, MUSTA) of stationary continuous-time stochastic processes with embedded point processes. It turns out that not only EPSTA and CEPSTA, but also MUSTA can be characterized by certain invariance...

Stationary random closed sets [Xi] in are considered whose realizations belong to the extended convex ring. A new approach is proposed to joint estimation of the specific intrinsic volumes of [Xi], including the specific Euler-Poincaré characteristic , the specific surface area , and the volume...

We give some probabilistic conditions based on coupling for a functional of a Poisson point process to be differentiable in the intensity [lambda] of this process in a neighborhood of the origin. These conditions are exemplified on various queueing theory problems, and compared with other...