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Error bounds for arbitrary approximations of “nearly reversible” Markov chains and a communications example. (English) Zbl 0914.60040

Author’s abstract: A condition is provided to conclude error bounds when using an arbitrary steady state approximation of a “nearly reversible” Markov chain. The error bound is of the form \(\Delta R\) where (i) \(\Delta\) can be computed by the approximation in order, (ii) \(R\) can be obtained analytically by the system of interest. The results will be illustrated for a communication system with different source characteristics. An approximation is suggested based on truncating the corresponding Möbius-function. An \(R\)-value is obtained by an inductive Markov reward equation. Numerical illustration indicates that the error bound can be useful for practical purposes.

MSC:

60J20 Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
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