Generalized Poisson Single Stack, Randomly Chosen And Decomposition

Poisson sheet is the basic, important Markov process with two parameters , and the generalizd Poisson sheet is an important generaliztion of Poisson sheet. Generalized Poisson sheet had been introduced and its properties had been researched in monograph [l] which is written by my director YangXiangQun. The sum, random selection and decomposition of Poisson sheet had been researched [ 9 ]. But the definition of random selection in (9)is ambiguous. Therefore, the formulation and proof of the conclusion are less rigorous and may be not correct. In this thesis, We dealt with the same problems for generalized Poisson sheet. The rigorous definition of random selection for generalized Poisson sheet is given. It is proved that the sum of independent generealized Poisson sheets which are limited in number is still a generalized Poisson sheet. The random selection for a generalized Poisson sheet is still a generalized Poisson sheet. Finally if we extendprobability space properly , a generalized Poissom sheet can be decomposed into some generalized Poisson sheets which are limited in number and sum of which is the original one.