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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Results 1-5 of 67
... follows . First , let X denote the random variable representing the time interval from a fixed time origin , say t = 0 , to the first subsequent point . Because the development of the process in the region t > 0 is independent of Ho ...
... follows from the strong independence properties of the Poisson process that the distribution of N ( a , b ) depends only on b - a . One proof of the Poisson distribution proceeds by writing N ( t ) = N ( 0 , t ) and P. ( t ) = pr { N ...
... follows . The chance that the origin falls in an interval of length in ( z , 2 + 8 ) is proportional to zg ( z ) 8 + 0 ( 8 ) and hence , on normalization , the density of the length of that interval is zg ( 2 ) / Hy , where lx E ( X ) ...
... follow notes on some of these generalizations , together with brief comments on the nature of the new ideas involved . ( i ) Multiple occurrences The special examples introduced in Section 1.2 are all such that points occur in isolation ...
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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 |