Reduced-memory likelihood processing of point processes

The problems of reduced-memory modeling and processing of regular point processes are studied. The -memory processes and processors are defined as those whose present (incremental) behavior depends only on the present observation of counts and the stored values of the preceding instants of occurrence. Characterization theorems for -memory point processes and homogeneous reduced-memory point processes are obtained. Under proper optimization criteria, optimal reduced-memory "moving-window" information processors for point processes are derived. The results are applied to study reduced-memory processors for doubly stochastic Poisson processes (DSPP\´s) and to characterize -memory DSPP\´s. Finally, a practically implementable scheme of a distribution-free l-memory processor is presented.