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Numerical solution of linear equations arising in Markov chain models. (English) Zbl 0757.65156

The authors examine several non-iterative methods for numerically solving the linear equation \(x=b+Qx\) that arises in the study of Markov chains. Here \(b\) is a vector of nonnegative constants and \(Q\) is a substochastic (not necessarily sparse) matrix, derived from a stochastic by deleting state 0.
The emphasis is done on moments of first-passage times and times to absorption. A comparison of methods on the basis of accuracy and computation leads to the conclusion that state-reduction is the most accurate and that the matrix solutions need the least computational time.

MSC:

65C99 Probabilistic methods, stochastic differential equations
65F05 Direct numerical methods for linear systems and matrix inversion
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
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