Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Cover of the book

2015 | OriginalPaper | Chapter

1. Poisson Point Processes

Author : Kiyosi Itô

Published in: Poisson Point Processes and Their Application to Markov Processes

Publisher: Springer Singapore

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

Throughout this note we will use the following notations. An interval of the type [l, r), \(-\infty < l < r \le \infty \) is called a time interval and is denoted by \(T, T_1, T_2, \ldots \). T is regarded as a measurable space associated with the topological \(\sigma \)-algebra on \(\mathscr {T}\) on T. \(\mathscr {T}_1, \mathscr {T}_2, \ldots \) are used respectively for those of \(T_1, T_2, \ldots \).

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
next chapter Application to Markov Processes
Footnotes
1
The random variable \(\equiv \infty \) is regarded to be Poisson distributed with mean \(\infty \).
 
2
With values in \(\{0,1,2,\dots \}\).
 
3
With values in \(T \times U (\mathscr {T} \times \mathscr {U})\).
 
4
\(\mathscr {C}\) is called semi-multiplicative if the intersection of two members in \(\mathscr {C}\) is expressed as a finite disjoint union of members in \(\mathscr {C}\).
 
Literature
1.
Itô, K.: Stochastic processes. In: Barndorff-Nielsen, O.E., Sato, K. (eds.) Lectures given at Aahus University, Springer (2004)
2.
Lévy, P.: Théorie de l’addition des variables aléatoires (2nd ed. 1954). Paris (1937)
Metadata
Title
Poisson Point Processes
Author
Kiyosi Itô
Copyright Year
2015
Publisher
Springer Singapore
Book
Poisson Point Processes and Their Application to Markov Processes

Print ISBN: 978-981-10-0271-7

Electronic ISBN: 978-981-10-0272-4

Copyright Year: 2015

DOI
https://doi.org/10.1007/978-981-10-0272-4_1