## 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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### References:

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