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 25
... space - time ( ii ) Non - interacting Poisson processes with birth , death and movement ( iv ) Processes with immigration ( v ) Systems with interaction Bibliographic notes , 6 Further results and exercises , 6 145 145 147 148 149 149 ...
... space arise in many fields of application and have been extensively studied in recent years from several points of view . In this book we aim to describe recent work on the properties of such probabilistic models , putting emphasis on ...
... space . A few outline examples illustrate the breadth of potential applications : ( i ) emissions from a radioactive source occur in an irregular sequence in time , each emission defining a time instant ; ( ii ) Fig . 1.1 shows a small ...
... space rather than in time occur , for example , in plant ecology , when a line transect is taken in a field and the ... spaces of two or more dimensions . There are three broad aspects to the theoretical study of point processes : ( a ) ...
... space , is associated with a point process , where a point is a time of transition , or , more generally , a time of entry into a pre - assigned state or set of states . Whether it is useful to look at a particular process in this way ...
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 |