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. |
From inside the book
Results 1-5 of 27
... time origin , the intervals X1 , X2 , ... between successive points are independently exponentially distributed with parameter p , which we call an interval specification ; ( c ) by the above specification of the joint 6 POINT PROCESSES.
D.R. Cox, Valerie Isham. ( c ) by the above specification of the joint distribution of N ( A1 ) , N ( A2 ) , ... for an arbitrary collection A1 , A2 , ... of non - overlapping sets on the time axis , which we call a counting ...
... joint distribution of the intervals between successive points , the interval specification ; ( iii ) via the joint distribution of the numbers of points in arbitrary sets A1 , A2 , ... , the counting specification . We shall consider ...
... joint distributions of counts in arbitrary sets ; these joint distributions may depend on any explanatory variables available . This definition is in line with the general definition of a stochastic process as being determined by the joint ...
... joint distribution of N ( A ) , N ( A2 ) , ... , N ( Ap ) is the same as that of N ( A , + T ) , N ( A2 + 1 ) , ... , N ( Ak + T ) for all 1 and k = 1 , 2 , ... , where A ++ is the set of time values formed by translating A by . As the ...
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 |