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 34
... Further results and exercises , 1 11 13 13 14 15 15 16 17 18 18 2 Theoretical framework 2.1 Some basic definitions 2.2 Stationarity 2.3 Orderliness 2.4 Palm distributions 2.5 Moments 2.6 Spectral properties 2.7 The probability ...
... Further results and exercises , 3 58 59 62 65 66 66 67 70 75 81 84 90 93 94 4 Operations on point processes 4.1 Preliminary remarks 4.2 Operational time 4.3 Thinning 4.4 Translation 4.5 Superposition 4.6 Infinite divisibility ...
... Further results and exercises , 5 123 124 126 128 131 134 134 135 136 139 140 141 143 143 6 Spatial processes 6.1 Preliminary remarks 6.2 Some simple generalizations of one - dimensional processes ( i ) Poisson processes ( ii ) Doubly ...
... Further , the above definition of the Poisson process implies that , starting from an arbitrary time origin , subsequent points are at times X1 , X1 + X2 , X1 + X2 + X 3 , ... , ( 1.6 ) where the random variables { X ; } are independent ...
... further in Chapter 2. For the Poisson process , the complete intensity function is a constant , the rate p . For a renewal process , the independence of the intervals between successive events implies that ( 1.10 ) involves H , only ...
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 |