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arbitrary argument assume asymptotic autocovariance bivariate class 2 points cluster centres complete intensity function conditional intensity function consider constant counter counting measure counts covariance defined denote density function density g dependent discussed distribution function doubly stochastic Poisson equation example exponential distribution finite follows forward recurrence function G Gaussian process given independent and identically infinitely divisible instant interval distribution interval sequence intervals between successive joint distribution Laplace transform linear self-exciting process Markov process number of points obtained orderly processes ordinary renewal process origin parameter particular points occur Poisson distribution probability density probability generating function process of cluster process of points process of rate random variables realization renewal process satisfies second-order properties semi-Markov process simple spatial special processes specified stationary process stochastic Poisson process stochastic process studied successive points superposition Suppose survivor function translation univariate point process upcrossings variance zero
Page 174 - Crame'r, H. (1966) . On the intersections between the trajectories of a normal stationary process and a high level. Ark. Mat.
Page 174 - Series expansions for the properties of a birth process of controlled variability.
Page 173 - Comparative aspects of the study of ordinary time series and of point processes.
Page 177 - Some models for stationary series of univariate events. In Stochastic Point Processes: Statistical Analysis, Theory and Applications (PAW Lewis, ed.).