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Mathematical Growth Model of Cluster Birth and Death Process with Immigration and Emigration

R.N. Rachmawati

Abstract


Stochastic model is a simplified form of the phenomena in the real world that involves the concept of probability. This model is considered more representatives because it is more dynamic in capturing natural indications involving the concept of space and time. This paper presents stochastic growth model of cluster birth and death process with the influence of immigration and emigration. It is driven by a number of real phenomena that can be represented by this process, for example the birth of new individuals and disease in certain place and time. To that end, the results of this paper are stochastic growth model of cluster birth and death process with the influence of immigration and emigration and differential equation of probability generating function for the process.

Keywords


Stochastic process, Poisson process, birth and death process, cluster birth and death process.

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