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 27
... called multivariate ; ( vii ) point processes occurring along a single dimension in space rather than in time occur , for example , in plant ecology , when a line transect is taken in a field and the position along it of plants of a ...
... called a non - homogeneous Poisson process . A closely related possibility is that there is an observed explanatory variable , z ( t ) say , and that the rate of the Poisson process at time t is a function of z ( t ) . For instance , in ...
... called the forward recurrence time from t = 0 , will not have the density g and that if we examine the process for t > 0 a modified renewal process will be obtained , but with a special form for g .. This special form can be calculated ...
... called an equilibrium renewal process . It can be shown directly from ( 1.9 ) that the equilibrium renewal process and the corresponding ordinary renewal process are identical if and only if g is exponential and the process is a Poisson ...
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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 |