This book describes the properties of stochastic probabilistic models and develops the applied mathematics of stochastic point processes. It is useful to students and research workers in probability and statistics and also to research workers wishing to apply stochastic point processes.
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alternative applications arbitrary argument arise assume asymptotic bivariate called Chapter class 2 points cluster centres cluster processes complete intensity function conditional intensity connection consider constant construction corresponding counter counts defined definition denote density dependent derived described detail determined dimension discussed equation equilibrium example finite follows further given gives identically distributed important independent and identically instant interval intervals between successive joint limit mark Markov mean measure multiple normal Note number of points obtained orderly origin parameter particular point process Poisson distribution Poisson process position possible probability generating function process of rate properties Prove random variables realization reference relation renewal process satisfies Section sequence shown simple space spatial process specification specified stationary statistical studied successive points superposition Suppose taking theory transform translation values 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.).