On dependent marking and thinning of point processes

Günter Last

Stochastic Processes and their Applications, 1993, vol. 45, issue 1, 73-94

Abstract: 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 applications we discuss, firstly, a shock model that is of relevance in the field of software reliability. Secondly, we derive a sufficient criterion guaranteeing that a marked point process can be represented as a thinning of another one. Thirdly, we prove a sufficient criterion ensuring that a real-valued jump process can be pathwise dominated by a second such process.

Date: 1993
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