We consider an expanding sparse dynamic network model where the time evolution is governed by a Markovian structure. Transition of the network from time $t$ to $t+1$ involves three parts : (i) a new node joins the existing network with a given probability of edge formation, (ii) existing edges drop out randomly with a fixed probability, and (iii) new edges are formed randomly among the existing nodes with a fixed probability. We consider long term behavior of the network density and establish its limit. We also derive asymptotic distributions of the maximum likelihood estimators of key model parameters and investigate properties of a parametric Bootstrap.
This is a joint work with Wei Zhao.
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