Displaying similar documents to “Spectral gap and convex concentration inequalities for birth–death processes”

Binomial-Poisson entropic inequalities and the M/M/ queue

Djalil Chafaï (2006)

ESAIM: Probability and Statistics

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This article provides entropic inequalities for binomial-Poisson distributions, derived from the two point space. They appear as local inequalities of the M/M/ queue. They describe in particular the exponential dissipation of -entropies along this process. This simple queueing process appears as a model of “constant curvature”, and plays for the simple Poisson process the role played by the Ornstein-Uhlenbeck process for Brownian Motion. Some of the inequalities are recovered...

Invariant measures and a stability theorem for locally Lipschitz stochastic delay equations

I. Stojkovic, O. van Gaans (2011)

Annales de l'I.H.P. Probabilités et statistiques

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We consider a stochastic delay differential equation with exponentially stable drift and diffusion driven by a general Lévy process. The diffusion coefficient is assumed to be locally Lipschitz and bounded. Under a mild condition on the large jumps of the Lévy process, we show existence of an invariant measure. Main tools in our proof are a variation-of-constants formula and a stability theorem in our context, which are of independent interest.

Transportation inequalities for stochastic differential equations of pure jumps

Liming Wu (2010)

Annales de l'I.H.P. Probabilités et statistiques

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For stochastic differential equations of pure jumps, though the Poincaré inequality does not hold in general, we show that 1 transportation inequalities hold for its invariant probability measure and for its process-level law on right continuous paths space in the 1-metric or in uniform metrics, under the dissipative condition. Several applications to concentration inequalities are given.