Geodesic
Monotonicity and comparison results for nonnegative dynamic systems. Part I: Discrete-time case
Kybernetika, Tome 42 (2006) no. 1, pp. 37-56.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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.
Classification : 37N40, 39A10, 60J10, 60J27, 90A16, 91B62
Keywords: Markov chains; monotonicity; nonnegative matrices 
@article{KYB_2006__42_1_a1,
     author = {Dijk, Nico M. van and Sladk\'y, Karel},
     title = {Monotonicity and comparison results for nonnegative dynamic systems. {Part} {I:} {Discrete-time} case},
     journal = {Kybernetika},
     pages = {37--56},
     publisher = {mathdoc},
     volume = {42},
     number = {1},
     year = {2006},
     mrnumber = {2208519},
     zbl = {1249.60168},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2006__42_1_a1/}
}
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
SP  - 37
EP  - 56
VL  - 42
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/KYB_2006__42_1_a1/
LA  - en
ID  - KYB_2006__42_1_a1
ER  - 
%0 Journal Article
%A Dijk, Nico M. van
%A Sladký, Karel
%T Monotonicity and comparison results for nonnegative dynamic systems. Part I: Discrete-time case
%J Kybernetika
%D 2006
%P 37-56
%V 42
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/KYB_2006__42_1_a1/
%G en
%F KYB_2006__42_1_a1
Dijk, Nico M. van; Sladký, Karel. Monotonicity and comparison results for nonnegative dynamic systems. Part I: Discrete-time case. Kybernetika, Tome 42 (2006) no. 1, pp. 37-56. http://geodesic.mathdoc.fr/item/KYB_2006__42_1_a1/