# Point Processes > Mediated Wiki article. Canonical URL: https://mediated.wiki/source/Point_Processes > Markdown URL: https://mediated.wiki/source/Point_Processes.md > Source: https://en.wikipedia.org/wiki/Point_Processes > Source revision: 1329527496 > License: Creative Commons Attribution-ShareAlike 4.0 International (https://creativecommons.org/licenses/by-sa/4.0/) {{Short description|1980 mathematics book by Cox and Isham}}{{Infobox book | author = [David Cox](/source/David_Cox_(statistician)), [Valerie Isham](/source/Valerie_Isham) | pub_date = 1980 | genre = Mathematics | publisher = [Chapman & Hall](/source/Chapman_%26_Hall) | image = File:Point_Processes.jpg }} {{Use dmy dates|cs1-dates=ly|date=October 2020}} {{italic title}} '''''Point Processes''''' is a book on the mathematics of [point process](/source/point_process)es, randomly located sets of points on the [real line](/source/real_line) or in other geometric spaces. It was written by [David Cox](/source/David_Cox_(statistician)) and [Valerie Isham](/source/Valerie_Isham), and published in 1980 by [Chapman & Hall](/source/Chapman_%26_Hall) in their Monographs on Applied Probability and Statistics book series. The Basic Library List Committee of the [Mathematical Association of America](/source/Mathematical_Association_of_America) has suggested its inclusion in undergraduate mathematics libraries.{{r|bll}} ==Topics== Although ''Point Processes'' covers some of the general theory of point processes, that is not its main focus, and it avoids any discussion of [statistical inference](/source/statistical_inference) involving these processes. Instead, its aim is to present the properties and descriptions of several specific processes arising in applications of this theory,{{r|biggins|holmes|daley|vere-jones}} which had not been previously collected in texts in this area.{{r|holmes}} Three of its six chapters concern more general material, while the final three are more specific. The first chapter includes introductory material on standard processes: [Poisson point process](/source/Poisson_point_process)es, [renewal process](/source/renewal_process)es, [self-exciting processes](/source/Hawkes_process), and [doubly stochastic processes](/source/doubly_stochastic_model). The second chapter provides some general theory including [stationarity](/source/stationary_process), orderliness (meaning that the probability of multiple arrivals in short intervals is sublinear in the interval length), [Palm distributions](/source/Palm_calculus), [Fourier analysis](/source/Fourier_analysis), and [probability-generating function](/source/probability-generating_function)s.{{r|daly}} Chapter four (the third of the more general chapters) concerns [point process operation](/source/point_process_operation)s, methods of modifying or combining point processes to generate other processes.{{r|vere-jones|daly}} Chapter three, the first of the three chapters on more specific models, is titled "Special models".{{r|vere-jones}} The special models that it covers include non-stationary Poisson processes, [compound Poisson process](/source/compound_Poisson_process)es, and the [Moran process](/source/Moran_process), along with additional treatment of doubly stochastic processes and renewal processes. Until this point, the book focuses on point processes on the real line (possibly also with a time dimension), but the two final chapters concern [multivariate](/source/Multivariate_analysis) processes and on point processes for higher dimensional spaces, including spatio-temporal processes and [Gibbs point processes](/source/Gibbs_measure).{{r|daly}} ==Audience and reception== The book is primarily a reference for researchers.{{r|biggins}} It could also be used to provide additional examples for a course on [stochastic process](/source/stochastic_process)es, or as the basis for an advanced seminar. Although it uses relatively little advanced mathematics, readers are expected to understand advanced calculus and have some familiarity with [probability theory](/source/probability_theory) and [Markov chain](/source/Markov_chain)s.{{r|holmes}} Writing some ten years after its original publication, reviewer Fergus Daly of [The Open University](/source/The_Open_University) writes that his copy has been well used, and that it "still is a very good book: lucid, relevant and still not matched in its approach by any other text".{{r|daly}} ==References== {{citation|title=''Point Processes'' (not yet reviewed)|url=https://www.maa.org/press/maa-reviews/point-processes|work=MAA Reviews|publisher=Mathematical Association of America|accessdate=2020-12-13}} {{citation | last = Biggins | first = J. D. | date = June 1981 | doi = 10.2307/3615757 | issue = 432 | journal = [The Mathematical Gazette](/source/The_Mathematical_Gazette) | jstor = 3615757 | page = 153 | title = Review of ''Point Processes'' | volume = 65}} {{citation | last = Daley | first = D. J. | journal = zbMATH | title = Review of ''Point Processes'' | zbl = 0441.60053}} {{citation | last = Daly | first = Fergus | doi = 10.2307/2983051 | issue = 2 | journal = [Journal of the Royal Statistical Society, Series A](/source/Journal_of_the_Royal_Statistical_Society%2C_Series_A) | jstor = 2983051 | pages = 358–359 | title = Review of ''Point Processes'' | volume = 154 | year = 1991}} {{citation | last = Holmes | first = Paul T. | date = June 1983 | doi = 10.2307/2288675 | issue = 382 | journal = Journal of the American Statistical Association | jstor = 2288675 | pages = 500–501 | title = none | volume = 78}} {{citation | last = Vere-Jones | first = David | author-link = David Vere-Jones | journal = [Mathematical Reviews](/source/Mathematical_Reviews) | mr = 0598033 | title = Review of ''Point Processes'' | year = 1982}} Category:Mathematics books Category:1980 non-fiction books Category:Point processes --- Adapted from the Wikipedia article [Point Processes](https://en.wikipedia.org/wiki/Point_Processes) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Point_Processes?action=history)). 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