An introduction to the theory of point processes

zbMath0657.60069MaRDI QIDQ1210821

D. Vere-Jones, Daryl J. Daley

Publication date: 5 June 1993

Published in: Springer Series in Statistics (Search for Journal in Brave)

zbMATH Keywords

point processesSpectral theoryinfinitely divisible processesPalm theorydoubly stochastic processesCluster processesmartingale approach to statistical inferencerandom integralssample-path propertiestheory of self-renewing aggregates

Mathematics Subject Classification ID

Random measures (60G57) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55) Research exposition (monographs, survey articles) pertaining to probability theory (60-02)

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III: General estimates for stationary ergodic random connected Lipschitz domains, Fluctuations and correlations for products of real asymmetric random matrices, A mechanistic spatio‐temporal modeling of COVID‐19 data, Minimax and adaptive tests for detecting abrupt and possibly transitory changes in a Poisson process, Stochastic homogenization on perforated domains. I: Extension operators, Stochastic homogenization on perforated domains II – Application to nonlinear elasticity models, Normal approximation of compound Hawkes functionals, Structural and hidden properties of 1D point processes: A wavelet-based study, Analytic computation of nonparametric Marsan–Lengliné estimates for Hawkes point processes, On Firing Rate Estimation for Dependent Interspike Intervals, Variational Latent Gaussian Process for Recovering Single-Trial Dynamics from Population Spike Trains, Third order point process intensity estimation for reaction time experiment data, Descending chains, the lilypond model, and mutual-nearest-neighbour matching, Stationary partitions and Palm probabilities, Normal approximation for random sums, Asymptotic properties of an empiricalK-function for inhomogeneous spatial point processes, Variational inference for Markovian queueing networks, On spatial matchings: The first-in-first-match case, Bayesian change points analysis on the seismic activity in northeastern Taiwan, Shape-driven nested Markov tessellations, Percolation of Hard Disks, Simplicial Homology of Random Configurations, Dimension reduction and homogenization of random degenerate operators. Part I, Asymptotic deficiency of score test for inhomogeneous Poisson processes, Fermionic observables in the transverse Ising chain, Morphometry of spatial patterns, Sharp constants in the Poisson approximation, Gibbs point processes for studying the development of spatial-temporal stochastic processes., Modeling cancer detection: Tumor size as a source of information on unobservable stages of carcinogenesis, Optimal asymptotic quadratic error of kernel estimators of Radon–Nikodym derivatives for strong mixing data, Point process models of rainfall: developments for fine-scale structure, Assessing Poisson Variation of Intestinal Tumour Multiplicity in Mice Carrying a Robertsonian Translocation, Flexible Modelling of Neuron Firing Rates Across Different Experimental Conditions: An Application to Neural Activity in the Prefrontal Cortex During a Discrimination Task, Multivariate Cox Hidden Markov models with an application to operational risk, Bartlett spectrum and mixing properties of infinitely divisible random measures, On Two Damage Accumulation Models and Their Size Effects, Asymptotic normality of the minimum distance estimators for a Poisson process with a discontinuous intensity function, Kinetic-Controlled Hydrodynamics for Traffic Models with Driver-Assist Vehicles, A global construction of homogeneous random planar tessellations that are stable under iteration, MCMC for normalized random measure mixture models, Second‐Order Analysis of Inhomogeneous Spatial Point Processes Using Case–Control Data, On a representation of partially-distinguishable populations, A New Nonlinear Sparse Component Analysis for a Biologically Plausible Model of Neurons, Crack STIT tessellations: characterization of stationary random tessellations stable with respect to iteration, Random dynamics and thermodynamic limits for polygonal Markov fields in the plane, A class of self-similar random measure, Power spectra of random spike fields and related processes, The dead leaves model: a general tessellation modeling occlusion, A renewal-process-type expression for the moments of inverse subordinators, Queues, stores, and tableaux, A martingale view of Blackwell’s renewal theorem and its extensions to a general counting process, Stability of spatial queueing systems, Convergence of Departures in Tandem Networks of·/GI/ ∞ Queues, Residual Analysis for Spatial Point Processes (with Discussion), Diffusion, super-diffusion and coalescence from a single step, Capacity and Error Exponents of Stationary Point Processes under Random Additive Displacements, Tails of Stopped Random Products: The Factoid and Some Relatives, Kernel Density Estimation on a Linear Network