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

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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 
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     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},
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     zbl = {1249.60169},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2006__42_2_a3/}
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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/