Point ProcessesThis 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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Contents
Theoretical framework | 21 |
Special models | 45 |
Operations on point processes | 97 |
Multivariate point processes | 117 |
Spatial processes | 143 |
| 173 | |
| 182 | |
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Common terms and phrases
A₁ arbitrary argument asymptotic autocovariance bivariate C₁ class 2 points cluster centres complete intensity function conditional intensity function consider constant counter counting measure counts covariance d₁ defined denote density g dependent discussed distribution function doubly stochastic Poisson equation equilibrium distribution example exponential distribution F₁ finite follows forward recurrence given H₁ independent and identically infinitely divisible instant interval distribution interval sequence intervals between successive joint distribution Laplace transform M₁ mark Markov process Markov property multivariate N₁ number of points obtained origin p₁ parameter particular point process points occur Poisson distribution probability density probability generating function process of points process of rate random variables renewal process Section semi-Markov process simple spatial process specification stationary process stochastic Poisson process stochastic process studied successive points superposition Suppose survivor function t₁ U₁ upcrossings variance X₁ zero ζη
Popular passages
Page 174 - Crame'r, H. (1966) . On the intersections between the trajectories of a normal stationary process and a high level. Ark. Mat.
Page 176 - Jacobs, PA and Lewis, PAW (1977). A mixed autoregressive-moving average exponential sequence and point process (EARMA(!, 1)).
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.).
Page 173 - Processus ponctuels et martingales: resultats recents sur la modelisation et le filtrage, Adv.