Point processes indexed by directed sets
Point processes are considered in the case where the carrier space is a directed set, not necessarily totally ordered. By extension of the carrier space, it is possible to construct a copy of the point process on a larger carrier space in which the points are now totally-ordered. This permits the construction of a martingale-based theory of point processes. The theory is an alternative to the general one of conditional intensities [see \textit{F. Papangelou}, Z. Wahrscheinlichkeitstheor. verw. Geb. 28, 207-226 (1974; Zbl 0271.60056)] or to the use of marked point processes for spaces like \({\mathbb{R}}^ k\) [see, for example, the reviewer, \textit{B. G. Ivanoff} and \textit{N. C. Weber}, Stochastic Processes Appl. 23, 307-318 (1986; Zbl 0614.60046)].
dual predictable projection. Point processes
martingale-based theory of point processes
scientific article; zbMATH DE number 4074108
scientific article