Random space change for multiparameter point processes
The author studies the problem of transforming a multiparameter point process \((N_ t\); \(t\in R^ n_+)\) into a Poisson process by means of random space change using compensators of the process. More precisely, under some regularity conditions on the i-compensator of N, \(i\in \{1,...,n\}\), the author shows that there exists a family of stopping sets \((D_ t\); \(t\in R^ n_+)\) such that \((\hat N_ t\); \(t\in R^ n_+)\) given by \(\hat N_ t=\int I_{D_ t}(s)dN_ s\) is a Poisson process. As shown by \textit{T. C. Brown}, \textit{B. G. Ivanoff} and \textit{N. C. Weber} [Stochastic Processes Appl. 23, 307-318 (1986; Zbl 0614.60046)] the property of the i-compensator to be deterministic characterizes the Poisson process in a similar way as in the one-parameter case. The author does not assume that N has an intensity.
scientific article; zbMATH DE number 4172073