Geodesic
Monotonicity and comparison results for nonnegative dynamic systems. Part II: Continuous-time case
Kybernetika, Tome 42 (2006) no. 2, pp. 161-180.

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

This second Part II, which follows a first Part I for the discrete-time case (see [DijkSl1]), deals with monotonicity and comparison results, as generalization of the pure stochastic case, for stochastic dynamic systems with arbitrary nonnegative generators in the continuous-time case. In contrast with the discrete-time case the generalization is no longer straightforward. A discrete-time transformation will therefore be developed first. Next, results from Part I can be adopted. The conditions, the technicalities and the results will be studied in detail for a reliability application that initiated the research. This concerns a reliability network with dependent components that can breakdown. A secure analytic performance bound is obtained.
Classification : 39A10, 60J27, 60K10, 90A16, 91B62
Keywords: Markov chains; monotonicity; nonnegative matrices 
@article{KYB_2006__42_2_a3,
     author = {Dijk, Nico M. van and Sladk\'y, Karel},
     title = {Monotonicity and comparison results for nonnegative dynamic systems. {Part} {II:} {Continuous-time} case},
     journal = {Kybernetika},
     pages = {161--180},
     publisher = {mathdoc},
     volume = {42},
     number = {2},
     year = {2006},
     mrnumber = {2241783},
     zbl = {1249.60169},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2006__42_2_a3/}
}
TY  - JOUR
AU  - Dijk, Nico M. van
AU  - Sladký, Karel
TI  - Monotonicity and comparison results for nonnegative dynamic systems. Part II: Continuous-time case
JO  - Kybernetika
PY  - 2006
SP  - 161
EP  - 180
VL  - 42
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/KYB_2006__42_2_a3/
LA  - en
ID  - KYB_2006__42_2_a3
ER  - 
%0 Journal Article
%A Dijk, Nico M. van
%A Sladký, Karel
%T Monotonicity and comparison results for nonnegative dynamic systems. Part II: Continuous-time case
%J Kybernetika
%D 2006
%P 161-180
%V 42
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/KYB_2006__42_2_a3/
%G en
%F KYB_2006__42_2_a3
Dijk, Nico M. van; Sladký, Karel. Monotonicity and comparison results for nonnegative dynamic systems. Part II: Continuous-time case. Kybernetika, Tome 42 (2006) no. 2, pp. 161-180. http://geodesic.mathdoc.fr/item/KYB_2006__42_2_a3/