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 23
... possible , in the hope that the book will be useful both to students and research workers in probability and statistics and also to research workers in other fields wishing to apply stochastic point processes . Some of the book was ...
... possible ; we exclude this possibility for the moment . If the process starts from time t = 0 , then a little care is needed with the initial conditions . If a point is known to have occurred at t = 0 , then we define a process in which ...
... possible to produce renewal processes with a wide range of qualitative behaviour , the renewal process remains very special because of the strong requirement that the intervals between successive events are mutually independent . ( iii ) ...
... possible physical interpretation is that a component of some system has periods of use and of idleness and that failure can occur only during a period of use . An alternative name for a doubly stochastic process is a process with random ...
... possible sets of time instants , subject to selfconsistency . In applications to special processes this is rarely a convenient starting point , in connection with either stochastic processes generally or point processes in particular ...
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 |