|
In statistics and probability theory, a point process is a type of random process for which any one realisation consists of a set of isolated points either in time or geographical space, or in even more general spaces. For example, the occurrence of lightning strikes might be considered as a point process in both time and geographical space if each is recorded according to its location in time and space. Point processes are well studied objects in probability theory〔Kallenberg, O. (1986). ''Random Measures'', 4th edition. Academic Press, New York, London; Akademie-Verlag, Berlin. ISBN 0-12-394960-2, .〕〔Daley, D.J, Vere-Jones, D. (1988). ''An Introduction to the Theory of Point Processes''. Springer, New York. ISBN 0-387-96666-8, .〕 and the subject of powerful tools in statistics for modeling and analyzing spatial data,〔Diggle, P. (2003). ''Statistical Analysis of Spatial Point Patterns'', 2nd edition. Arnold, London. ISBN 0-340-74070-1.〕〔Baddeley, A. (2006). Spatial point processes and their applications. In A. Baddeley, I. Bárány, R. Schneider, and W. Weil, editors, ''Stochastic Geometry: Lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, September 13–18, 2004'', Lecture Notes in Mathematics 1892, Springer. ISBN 3-540-38174-0, pp. 1–75〕 which is of interest in such diverse disciplines as forestry, plant ecology, epidemiology, geography, seismology, materials science, astronomy, telecommunications, computational neuroscience,〔Brown, E. N., Kass, R. E., & Mitra, P. P. (2004). Multiple neural spike train data analysis: state-of-the-art and future challenges. Nature Neuroscience, 7, 456–461. doi:10.1038/nn1228.〕 economics〔Robert F. Engle and Asger Lunde, 2003, "Trades and Quotes: A Bivariate Point Process". Journal of Financial Econometrics Vol. 1, No. 2, pp. 159–188〕 and others. Point processes on the real line form an important special case that is particularly amenable to study,〔Last, G., Brandt, A. (1995).''Marked point processes on the real line: The dynamic approach.'' Probability and its Applications. Springer, New York. ISBN 0-387-94547-4, 〕 because the points are ordered in a natural way, and the whole point process can be described completely by the (random) intervals between the points. These point processes are frequently used as models for random events in time, such as the arrival of customers in a queue (queueing theory), of impulses in a neuron (computational neuroscience), particles in a Geiger counter, location of radio stations in a telecommunication network〔Gilbert, E.N. (1961) Random plane networks. ''SIAM Journal'', Vol. 9, No. 4.〕 or of searches on the world-wide web. ==General point process theory== In mathematics, a point process is a random element whose values are "point patterns" on a set ''S''. While in the exact mathematical definition a point pattern is specified as a locally finite counting measure, it is sufficient for more applied purposes to think of a point pattern as a countable subset of ''S'' that has no limit points. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「point process」の詳細全文を読む スポンサード リンク
|