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 66
... examples ( i ) Poisson processes ( ii ) Renewal processes ( iii ) Linear self - exciting processes ( iv ) Doubly stochastic Poisson processes 1.3 The specification and properties of point processes 1.4 Some generalizations ( i ) ...
... example that the points occur in some region of space . A few outline examples illustrate the breadth of potential ... example , in ( iv ) , we may distinguish two classes , cars and lorries . In a queueing problem , ( v ) , there may be ...
... example , in plant ecology , when a line transect is taken in a field and the position along it of plants of a particular species is noted . Such applications give rise also in an obvious way to point processes in spaces of two or more ...
... examples The properties of a variety of special processes important in applications will be studied in Chapter 3. In the present section , using a temporal approach , we outline properties of four special types of process , mainly in ...
... example to represent situations with a time trend or cyclical fluctuations in the rate of occurrence , it is useful to replace the constant p by a function of time , p ( t ) , say , the other assumptions remaining the same . This gives ...
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 |