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Point process calculus in time and s...

Bremaud, Pierre.

Point process calculus in time and spacean introduction with applications /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Point process calculus in time and spaceby Pierre Bremaud.
其他題名:	an introduction with applications /
作者:	Bremaud, Pierre.
出版者:	Cham :Springer International Publishing :2020.
面頁冊數:	xiii, 556 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Point processes.
電子資源:	https://doi.org/10.1007/978-3-030-62753-9
ISBN:	9783030627539$q(electronic bk.)

Point process calculus in time and spacean introduction with applications /
Bremaud, Pierre.

Point process calculus in time and spacean introduction with applications /[electronic resource] :by Pierre Bremaud. - Cham :Springer International Publishing :2020. - xiii, 556 p. :ill., digital ;24 cm. - Probability theory and stochastic modelling,v.982199-3130 ;. - Probability theory and stochastic modelling ;v.70..

Introduction -- Generalities -- Poisson Process on the Line -- Spatial Poisson Processes -- Renewal and Regenerative Processes -- Point Processes with a Stochastic Intensity -- Exvisible Intensity of Finite Point Processes -- Palm Probability on the Line -- Palm Probability in Space -- The Power Spectral Measure -- Information Content of Point Processes -- Point Processes in Queueing -- Hawkes Point Processes -- Appendices -- Bibliography -- Index.

This book provides an introduction to the theory and applications of point processes, both in time and in space. Presenting the two components of point process calculus, the martingale calculus and the Palm calculus, it aims to develop the computational skills needed for the study of stochastic models involving point processes, providing enough of the general theory for the reader to reach a technical level sufficient for most applications. Classical and not-so-classical models are examined in detail, including Poisson-Cox, renewal, cluster and branching (Kerstan-Hawkes) point processes.The applications covered in this text (queueing, information theory, stochastic geometry and signal analysis) have been chosen not only for their intrinsic interest but also because they illustrate the theory. Written in a rigorous but not overly abstract style, the book will be accessible to earnest beginners with a basic training in probability but will also interest upper graduate students and experienced researchers.

ISBN: 9783030627539$q(electronic bk.)

Standard No.: 10.1007/978-3-030-62753-9doiSubjects--Topical Terms:

182289
Point processes.

LC Class. No.: QA274.42

Dewey Class. No.: 519.23

Point process calculus in time and spacean introduction with applications /
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245 1 0 $a Point process calculus in time and space $h [electronic resource] : $b an introduction with applications / $c by Pierre Bremaud.
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505 0 $a Introduction -- Generalities -- Poisson Process on the Line -- Spatial Poisson Processes -- Renewal and Regenerative Processes -- Point Processes with a Stochastic Intensity -- Exvisible Intensity of Finite Point Processes -- Palm Probability on the Line -- Palm Probability in Space -- The Power Spectral Measure -- Information Content of Point Processes -- Point Processes in Queueing -- Hawkes Point Processes -- Appendices -- Bibliography -- Index.
520 $a This book provides an introduction to the theory and applications of point processes, both in time and in space. Presenting the two components of point process calculus, the martingale calculus and the Palm calculus, it aims to develop the computational skills needed for the study of stochastic models involving point processes, providing enough of the general theory for the reader to reach a technical level sufficient for most applications. Classical and not-so-classical models are examined in detail, including Poisson-Cox, renewal, cluster and branching (Kerstan-Hawkes) point processes.The applications covered in this text (queueing, information theory, stochastic geometry and signal analysis) have been chosen not only for their intrinsic interest but also because they illustrate the theory. Written in a rigorous but not overly abstract style, the book will be accessible to earnest beginners with a basic training in probability but will also interest upper graduate students and experienced researchers.
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