Population Groups on a Graph

F. Etienne De Vylder

Chapter Chapter 16 in Life Insurance Theory, 1997, pp 139-156 from Springer

Abstract: Abstract We assume that the states of a graph are occupied by n individuals. We denote by tN α ° the number of individuals in state α at time t. The evolution of the population groups results from the following rules defining the closed graph model. At origin t=0, all n individuals are in state α=0 and all other states are void: 1 $$ {}_0{N_0}^o = n,{}_0{N_\alpha }^o = 0\left( {\alpha \ne 0} \right). $$ At any moment τ, any individual in state a can jump to a state β∈α′. The probability that this jump occurs during time interval dt equals τµα→β dτ. Jumps akin to different individuals are independent. No individuals from outside join the graph and no individuals from the graph leave it.

Date: 1997
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DOI: 10.1007/978-1-4757-2616-9_16

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