Point Processes and Their Statistical Inference |
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analogous assume assumptions asymptotic normality C+(E calculate central limit theorem Chapter compact computation conditional convergence in distribution covariance function Cox processes defined Definition distribution F distribution function empirical processes equation Example Exercise exvisible finite Gaussian H₁ hazard function hence hypotheses i.i.d. copies i.i.d. random independent increments infinitely divisible interarrival distribution Karr likelihood function likelihood ratio marked point process Markov process martingale martingale estimators martingale method maximum likelihood estimator mean measure metric entropy mixed Poisson processes N₁ nonparametric o-algebra p-thinning P₁ Palm distributions parameter Poisson process probability law problem process on R+ Proof Proposition Prove pseudo-state estimators random elements random measure random variables renewal process respect satisfying Section sequence space spectral stationary point process statistical inference stochastic intensity stochastic processes structure subset Suppose surely Wiener process zero