Stationary Random Processes Associated with Point Processes:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
New York, NY
Springer US
1981
|
| Series: | Lecture Notes in Statistics
5 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | In this set of notes we study a notion of a random process assoc- ted with a point process. The presented theory was inSpired by q- ueing problems. However it seems to be of interest in other branches of applied probability, as for example reliability or dam theory. Using developed tools, we work out known, aswell as new results from queueing or dam theory. Particularly queues which cannot be treated by standard techniques serve as illustrations of the theory. In Chapter 1 the preliminaries are given. We acquaint the reader with the main ideas of these notes, introduce some useful notations, concepts and abbreviations. He also recall basic facts from ergodic theory, an important mathematical tool employed in these notes. Finally some basic notions from queues are reviewed. Chapter 2 deals with discrete time theory. It serves two purposes. The first one is to let the reader get acquainted with the main lines of the theory needed in continuous time without being bothered by tech nical details. However the discrete time theory also seems to be of interest itself. There are examples which have no counte~ in continuous time. Chapter 3 deals with continuous time theory. It also contains many basic results from queueing or dam theory. Three applications of the continuous time theory are given in Chapter 4. We show how to use the theory in order to get some useful bounds for the stationary distribution of a random process |
| Physical Description: | 1 Online-Ressource (139p) |
| ISBN: | 9781468462685 9780387905754 |
| ISSN: | 0930-0325 |
| DOI: | 10.1007/978-1-4684-6268-5 |
Staff View
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| spelling | Rolski, Tomasz Verfasser aut Stationary Random Processes Associated with Point Processes by Tomasz Rolski New York, NY Springer US 1981 1 Online-Ressource (139p) txt rdacontent c rdamedia cr rdacarrier Lecture Notes in Statistics 5 0930-0325 In this set of notes we study a notion of a random process assoc- ted with a point process. The presented theory was inSpired by q- ueing problems. However it seems to be of interest in other branches of applied probability, as for example reliability or dam theory. Using developed tools, we work out known, aswell as new results from queueing or dam theory. Particularly queues which cannot be treated by standard techniques serve as illustrations of the theory. In Chapter 1 the preliminaries are given. We acquaint the reader with the main ideas of these notes, introduce some useful notations, concepts and abbreviations. He also recall basic facts from ergodic theory, an important mathematical tool employed in these notes. Finally some basic notions from queues are reviewed. Chapter 2 deals with discrete time theory. It serves two purposes. The first one is to let the reader get acquainted with the main lines of the theory needed in continuous time without being bothered by tech nical details. However the discrete time theory also seems to be of interest itself. There are examples which have no counte~ in continuous time. Chapter 3 deals with continuous time theory. It also contains many basic results from queueing or dam theory. Three applications of the continuous time theory are given in Chapter 4. We show how to use the theory in order to get some useful bounds for the stationary distribution of a random process Mathematics Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik Stationärer Prozess (DE-588)4056989-5 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Punktprozess (DE-588)4138173-7 gnd rswk-swf Stationärer Prozess (DE-588)4056989-5 s Punktprozess (DE-588)4138173-7 s 1\p DE-604 Stochastischer Prozess (DE-588)4057630-9 s 2\p DE-604 https://doi.org/10.1007/978-1-4684-6268-5 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Rolski, Tomasz Stationary Random Processes Associated with Point Processes Mathematics Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik Stationärer Prozess (DE-588)4056989-5 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Punktprozess (DE-588)4138173-7 gnd |
| subject_GND | (DE-588)4056989-5 (DE-588)4057630-9 (DE-588)4138173-7 |
| title | Stationary Random Processes Associated with Point Processes |
| title_auth | Stationary Random Processes Associated with Point Processes |
| title_exact_search | Stationary Random Processes Associated with Point Processes |
| title_full | Stationary Random Processes Associated with Point Processes by Tomasz Rolski |
| title_fullStr | Stationary Random Processes Associated with Point Processes by Tomasz Rolski |
| title_full_unstemmed | Stationary Random Processes Associated with Point Processes by Tomasz Rolski |
| title_short | Stationary Random Processes Associated with Point Processes |
| title_sort | stationary random processes associated with point processes |
| topic | Mathematics Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik Stationärer Prozess (DE-588)4056989-5 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Punktprozess (DE-588)4138173-7 gnd |
| topic_facet | Mathematics Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik Stationärer Prozess Stochastischer Prozess Punktprozess |
| url | https://doi.org/10.1007/978-1-4684-6268-5 |
| work_keys_str_mv | AT rolskitomasz stationaryrandomprocessesassociatedwithpointprocesses |