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• W2897664438 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 ℝ N . 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." @default.
• W2897664438 created "2018-10-26" @default.
• W2897664438 creator A5032787503 @default.
• W2897664438 creator A5053044735 @default.
• W2897664438 date "2014-03-01" @default.
• W2897664438 modified "2023-10-18" @default.
• W2897664438 title "Stability of Multi-Dimensional Birth-and-Death Processes with State-Dependent 0-Homogeneous Jumps" @default.
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• W2897664438 doi "https://doi.org/10.1017/s0001867800006935" @default.
• W2897664438 hasPublicationYear "2014" @default.
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