Characterization of spatial Poisson process along optional increasing paths. A problem of dimension's reduction
The paper investigates the problem of dimension reduction of a plane Poisson process by considering this process along optional increasing paths (OIPs). A convenient characterization of the spatial Poisson process is obtained on the basis of a suitable reparametrization of an OIP that succeeds to transform the process along the path into a one-parameter Poisson process. The key idea within the proof of these results is based on similar facts that hold for one-parameter martingales stopped by a family of bounded stopping times.
scientific article; zbMATH DE number 1395192