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dc.contributor.author
Jonckheere, Matthieu Thimothy Samson
dc.contributor.author
Shneer, Seva
dc.date.available
2017-06-23T21:06:59Z
dc.date.issued
2014-03
dc.identifier.citation
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
dc.identifier.issn
0001-8678
dc.identifier.uri
http://hdl.handle.net/11336/18829
dc.description.abstract
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.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Cambridge University Press
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
Stability Analysis
dc.subject
Birth And Death Processes
dc.subject
Lyapunov Functions
dc.subject
Stochastic Networks
dc.subject.classification
Estadística y Probabilidad
dc.subject.classification
Matemáticas
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
dc.title
Stability of multi-dimensional birth-and-death processes with state-dependent 0-homogeneous jumps
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2017-06-23T14:12:30Z
dc.identifier.eissn
1475-6064
dc.journal.volume
46
dc.journal.number
1
dc.journal.pagination
59-75
dc.journal.pais
Reino Unido
dc.journal.ciudad
Cambridge
dc.description.fil
Fil: Jonckheere, Matthieu Thimothy Samson. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santalo". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santalo"; Argentina
dc.description.fil
Fil: Shneer, Seva. Heriot-Watt University; Reino Unido
dc.journal.title
Advances In Applied Probability
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/https://doi.org/10.1017/S0001867800006935
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://www.cambridge.org/core/journals/advances-in-applied-probability/article/stability-of-multi-dimensional-birth-and-death-processes-with-state-dependent-0-homogeneous-jumps/CA2AC6770A5C9D69BA0DC593156DAAC6
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/0910.5851
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