Some Poisson approximations using compensators

DOI10.1214/AOP/1176993517zbMath0551.60048OpenAlexW2062479869MaRDI QIDQ801392

Timothy C. Brown

Publication date: 1983

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aop/1176993517

zbMATH Keywords

discrete approximationmarked point processescompound Poisson approximationscompensatorsthinning of point processes

Mathematics Subject Classification ID

Martingales with continuous parameter (60G44) General theory of stochastic processes (60G07) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

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Signed Poisson approximations for Markov chains ⋮ Convergence of thinning processes using compensators ⋮ A CUMULATIVE RESIDUAL INACCURACY MEASURE FOR COHERENT SYSTEMS AT COMPONENT LEVEL AND UNDER NONHOMOGENEOUS POISSON PROCESSES ⋮ Partitions of point processes: Multivariate Poisson approximations ⋮ On Stein-Chen factors for Poisson approximation ⋮ Poisson approximations of multinomial distributions and point processes ⋮ Poisson approximations for time-changed point processes ⋮ A new approach to Poisson approximation of simple point processes using compensators ⋮ Some poisson approximations for departure processes in general queueing networks ⋮ Pseudo-Poisson approximation for Markov chains ⋮ Poisson approximations for Markov-driven point processes ⋮ Coupling with compensators ⋮ Discriminating between sequences of bernoulli and markov-bernoulli trials ⋮ On the asymptotics of locally dependent point processes ⋮ A polynomial birth-death point process approximation to the Bernoulli process ⋮ On the optimality of multivariate Poisson approximation ⋮ Existence, uniqueness and approximation of the jump-type stochastic Schrödinger equation for two-level systems ⋮ Poisson approximation, compensators and coupling ⋮ A Poisson Limit Theorem for Reliability Models Based on Markov Chains ⋮ Poisson approximation ⋮ Asymptotic reliability of a linearly connected system with an infinite number of components

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