Generalized Ji(?)ina Process’s Extinction Rate And Simulation

This paper mainly discusses the continuous states space population size de-pendent branching process’s(abbr:CPSDBP) extinction rate in the almost surely extinction situation,and gives the sufficient condition for the process which is the CPSDBP after normalized by this rate convergent to a none zero random variable in the sense of almost surely and L2.Moreover,we give a numerical example which is not trivial and satisfies all the criterion above and a broad idea to the numerical simulation for the process’s first-order moment and second-order moment in this example. Meanwhile,we show the explosion rate of the CPSDBP in the situation that it has a positive probability to convergent to infinite.and the sufficient con-dition for the CPSDBP after normalized by the explosion rate convergent to a non-degenerate random variable in the sense of almost surely and L2.