Quasistationary Distributions for Level - Dependentquasi - Birth
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چکیده
We consider the problem of identifying the-invariant measures and hence the quasistationary distributions of an absorbing level-dependent quasi-birth-and-death process (QBD); that is, an absorbing Markov chain with a block-tridiagonal transition matrix P. We examine successive lower truncations of P, obtained by removing rows and columns corresponding to levels. The crucial factors in our technique are the Perron-Frobenius eigenvalue 1 of a fundamental matrix and the sequence f ` g of convergence norms of the successive lower truncations: 1 is the convergence norm of the transient class. We construct a-invariant measure for all < 1. When = 1 , we show that a QBD admits one of two types of-invariant measure: which type depends on whether 1 < 1 or 1 = 1. Together with a knowledge of whether 1 < 2 or 1 = 2 , this is suucient to give the-classiication of the process.
منابع مشابه
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تاریخ انتشار 1998