Artículo
Stability of multi-dimensional birth-and-death processes with state-dependent 0-homogeneous jumps
Fecha de publicación:
03/2014
Editorial:
Cambridge University Press
Revista:
Advances In Applied Probability
ISSN:
0001-8678
e-ISSN:
1475-6064
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
We study the conditions for positive recurrence and transience of multi-dimensional birth-and-death processes describing the evolution of a large class of stochastic systems, a typical example being the randomly varying number of flow-level transfers in a telecommunication wire-line or wireless network. First, using an associated deterministic dynamical system, we provide a generic method to construct a Lyapunov function when the drift is a smooth function on ℝN. This approach gives an elementary and direct proof of ergodicity. We also provide instability conditions. Our main contribution consists of showing how discontinuous drifts change the nature of the stability conditions and of providing generic sufficient stability conditions having a simple geometric interpretation. These conditions turn out to be necessary (outside a negligible set of the parameter space) for piecewise constant drifts in dimension two.
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Articulos de INSTITUTO DE INVESTIGACIONES MATEMATICAS "LUIS A. SANTALO"
Articulos de INSTITUTO DE INVESTIGACIONES MATEMATICAS "LUIS A. SANTALO"
Citación
Jonckheere, Matthieu Thimothy Samson; Shneer, Seva; Stability of multi-dimensional birth-and-death processes with state-dependent 0-homogeneous jumps; Cambridge University Press; Advances In Applied Probability; 46; 1; 3-2014; 59-75
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