## Point ProcessesThere has been much recent research on the theory of point processes, i.e., on random systems consisting of point events occurring in space or time. Applications range from emissions from a radioactive source, occurrences of accidents or machine breakdowns, or of electrical impluses along nerve fibres, to repetitive point events in an individual's medical or social history. Sometimes the point events occur in space rather than time and the application here raneg from statistical physics to geography. The object of this book is to develop the applied mathemathics of point processes at a level which will make the ideas accessible both to the research worker and the postgraduate student in probability and statistics and also to the mathemathically inclined individual in another field interested in using ideas and results. A thorough knowledge of the key notions of elementary probability theory is required to understand the book, but specialised "pure mathematical" coniderations have been avoided. |

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arbitrary argument assume asymptotic autocovariance bivariate class 2 points cluster centres complete intensity function conditional intensity function consider constant counter counts covariance defined denote density g dependent discussion distribution function distribution of mean doubly stochastic Poisson equation equilibrium distribution example exponential distribution finite follows forward recurrence given ℋt independent and identically infinitely divisible instant interval distribution interval sequence intervals between successive Isham J. R. Statist joint distribution Laplace transform Lewis Markov chain Markov process Markov property mathematical multiple occurrences number of points obtained ordinary renewal process origin parameter particular points occur Poisson distribution Prob probability density probability generating function process of points process of rate random variables renewal process Renewal theory second-order properties semi-Markov process simple space spatial process specification stationary process Stochastic Point Processes stochastic Poisson process stochastic process studied successive points superposition Suppose survivor function theory translation upcrossings variance zero