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 approximation arbitrary argument arise assume asymptotic bivariate called Chapter class 2 points cluster centres cluster processes conditional intensity connection consider constant construction corresponding counter counts defined denote density dependent derived described detail determined dimension discussed doubly stochastic equation equilibrium example finite follows further given gives identically distributed important independent and identically infinitely instant interval intervals between successive introduced joint limit marginal mark Markov mean measure normal Note number of points obtained occur orderly origin parameter particular physics point process Poisson distribution Poisson process position possible probability generating function process of rate properties Prove random variables realization recorded renewal process satisfies Section sequence shown simple space spatial process specified stationary studied successive points superposition Suppose theory transform translation 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.).