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 36
... random variables { X ; } are independent and identically distributed with the exponential distribution ( 1.4 ) . This property provides an alternative definition of the Poisson process , and a convenient way of simulating it . Note from ...
... random variables N ( A1 ) , N ( A2 ) , ... have independent Poisson distributions of means plAil , plAzl ..... In fact , the Poisson process could be defined by any one of the following mutually equivalent properties : ( a ) by the ...
... random environment . Now in principle this process can be expressed in terms of H , only , in fact p ( t ; H ) = E ... variables denoted at time t by the vector z ( t ) . Suppose that in addition there is an unobserved stochastic process ...
... random variables associated with a point process are the forward and backward recurrence times measured from t . These are respectively the time measured forward from t to the next point , and the time measured backwards from t to the ...
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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 |