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 31
... of mean plb - a ) and that N ( A ) has a Poisson distribution of mean p Al ... intervals have independent Poisson distributions . The distribution of N ( A ) ... between successive points are independently exponentially distributed with ...
... time X from the origin to the next point is uniformly distributed over ( 0 , 2 ) ... intervals but not their independence . Thus ( 1.9 ) applies more generally ... between successive events are mutually independent . ( iii ) Linear self ...
... of the intervals between successive events implies that ( 1.10 ) involves H , only through the time from t back to the point , if any , immediately preceding t . It is natural to build up simple processes by supposing plt ; H , ) to ...
... of ( 1.15 ) and ( 1.11 ) plus a specification of the properties of the ... between the levels 0 and 1. That is , the final point process , which is all ... intervals between successive points , the interval specification ; ( iii ) ...
... of the problems to be studied amount to interrelating the different specifications . For instance , if a process is conveniently specified by an intensity , what can be said about the intervals between successive points and about 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 |