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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... position of each vehicle as specified by a point , e.g. by the position of its front wheels , we have a point process in one - dimensional space , rather than in time ; ( v ) many of the stochastic problems of operational research ...
... position along it of plants of a particular species is noted . Such applications give rise also in an obvious way to point processes in spaces of two or more dimensions . There are three broad aspects to the theoretical study of point ...
... positions of all points in ( -00 , t ] . For u < v , let N ( u , v ) be a random variable giving the number of points in ( u , v ) . Then for a given positive constant P , with dimensions [ time ] ยป !, the Poisson process of rate p is ...
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Contents
1 | |
2 Theoretical framework | 21 |
3 Special models | 45 |
4 Operations on point processes | 97 |
5 Multivariate point processes | 117 |
6 Spatial processes | 143 |
References | 173 |
Author index | 182 |
Subject index | 184 |