Monotonicity and comparison results for nonnegative dynamic systems. Part I: Discrete-time case

Dijk, Nico M. van, and Sladký, Karel. "Monotonicity and comparison results for nonnegative dynamic systems. Part I: Discrete-time case." Kybernetika 42.1 (2006): 37-56. <http://eudml.org/doc/33791>.

@article{Dijk2006,
abstract = {In two subsequent parts, Part I and II, monotonicity and comparison results will be studied, as 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 the present 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 essential for the more practical continuous-time case in Part II (see [DijkSl2]). An instructive discrete-time random walk example is included.},
author = {Dijk, Nico M. van, Sladký, Karel},
journal = {Kybernetika},
keywords = {Markov chains; monotonicity; nonnegative matrices; Markov chains; monotonicity; nonnegative matrix},
language = {eng},
number = {1},
pages = {37-56},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Monotonicity and comparison results for nonnegative dynamic systems. Part I: Discrete-time case},
url = {http://eudml.org/doc/33791},
volume = {42},
year = {2006},
}

TY - JOUR
AU - Dijk, Nico M. van
AU - Sladký, Karel
TI - Monotonicity and comparison results for nonnegative dynamic systems. Part I: Discrete-time case
JO - Kybernetika
PY - 2006
PB - Institute of Information Theory and Automation AS CR
VL - 42
IS - 1
SP - 37
EP - 56
AB - In two subsequent parts, Part I and II, monotonicity and comparison results will be studied, as 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 the present 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 essential for the more practical continuous-time case in Part II (see [DijkSl2]). An instructive discrete-time random walk example is included.
LA - eng
KW - Markov chains; monotonicity; nonnegative matrices; Markov chains; monotonicity; nonnegative matrix
UR - http://eudml.org/doc/33791
ER -