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**Monotonicity and comparison results for nonnegative dynamic systems. I: Discrete-time case.**
*(English)*
Zbl 1249.60168

Summary: In two subsequent parts, monotonicity and comparison results will be studied, as a generalization of the pure stochastic case for arbitrary dynamic systems governed by nonnegative matrices. Part I covers the discrete-time and Part II the continuous-time case. The research has initially been motivated by a reliability application contained in Part II.

In Part I, it is shown that monotonicity and comparison results, as known for Markov chains, do carry over rather smoothly to the general nonnegative case for marginal, total and average reward structures. These results, though straightforward, are not only of theoretical interest by themselves, but also are essential for the more practical continuous-time case in Part II (see [Kybernetika 42, No. 2, 161-180 (2006; Zbl 1249.60169)]). An instructive discrete-time random walk example is included.

In Part I, it is shown that monotonicity and comparison results, as known for Markov chains, do carry over rather smoothly to the general nonnegative case for marginal, total and average reward structures. These results, though straightforward, are not only of theoretical interest by themselves, but also are essential for the more practical continuous-time case in Part II (see [Kybernetika 42, No. 2, 161-180 (2006; Zbl 1249.60169)]). An instructive discrete-time random walk example is included.

### Citations:

Zbl 1249.60169
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\textit{N. M. van Dijk} and \textit{K. Sladký}, Kybernetika 42, No. 1, 37--56 (2006; Zbl 1249.60168)

### References:

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