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 65
... points in ( -00 , t ] . For u < v , let N ( u , v ) be a random variable giving the number of points in ( u , v ) . Then for a given positive constant P , with dimensions [ time ] ยป !, the Poisson process of rate p is defined by the ...
... point in ( t , t +8 ] does not depend on whether there have been relatively few or relatively many points just before t ... number of men employed at time t , or some other index of unit of risk at time t , and we may consider a model in ...
... points are at times X1 , X1 + X2 , X1 + X2 + X 3 , ... , ( 1.6 ) where the random variables { X ; } are independent and ... number , N ( a , b ) , of points in a fixed interval ( a , b ) ; slightly more generally we may consider an ...
... numbers of points in a collection of nonoverlapping intervals have independent Poisson distributions . The distribution of N ( A ) for an arbitrary set A follows on expressing A as a union of a finite ( or countably infinite ) number of ...
... points add together . Let w ( x ) be a non - negative weight function defined for x 20 and let points occur at times ... number of points from a time origin in the remote past . In this notation the number of points in ( a , b ) , for b ...
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 |