FILTERED PROCESS AND ITS TWO CENTRAL LIMIT THEOREMS

The factorial cumulant measure and generating functional of point process are discussed in this paper. The relation between generating functional of point process and characteristic functional of filtered process with this point process as a primary process is obtained. Two central limit theorems on filtered process are given, which is the main result in this paper. The first one Th, 3. 4 is the theorem in §64 when applied to shot process. The second one Th. 4. 1 weakens the conditions of Th. 4. 1. 2 in 5