Applied stochastic processes:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York
Springer
2007
|
| Series: | Universitext
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 382 S. |
| ISBN: | 0387341714 9780387341712 |
Staff View
MARC
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| 245 | 1 | 0 | |a Applied stochastic processes |c Mario Lefebvre |
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Record in the Search Index
| _version_ | 1804136521210527744 |
|---|---|
| adam_text | Contents
Preface
........................................................
vii
List of Tables
.................................................. xi
List of Figures
.................................................xiii
1
Review of Probability Theory
............................. 1
1.1
Elementary probability
................................... 1
1.2
Random variables
....................................... 8
1.3
Random vectors
......................................... 21
1.4
Exercises
............................................... 34
2
Stochastic Processes
....................................... 47
2.1
Introduction and definitions
.............................. 47
2.2
Stationarity
............................................. 52
2.3
Ergodicity
.............................................. 55
2.4
Gaussian and Markovian processes
......................... 58
2.5
Exercises
............................................... 65
3
Markov Chains
............................................ 73
3.1
Introduction
............................................ 73
3.2
Discrete-time Markov chains
.............................. 77
3.2.1
Definitions and notations
........................... 77
3.2.2
Properties
........................................ 85
3.2.3
Limiting probabilities
.............................. 94
3.2.4
Absorption problems
...............................100
3.2.5
Branching processes
...............................104
3.3
Continuous-time Markov chains
...........................109
3.3.1
Exponential and gamma distributions
................109
3.3.2
Continuous-time Markov chains
.....................121
3.3.3
Calculation of the transition function Pij(t)
..........124
x
Contents
3.3.4
Particular processes
...............................
129
3.3.5
Limiting probabilities
and balance
equations
..........138
3.4
Exercises
...............................................
143
4
Diffusion Processes
........................................
ί
°
4.1
The Wiener process
......................................
173
4.2
Diffusion processes
.......................................
1°*
4.2.1
Brownian motion with drift
.........................
183
4.2.2
Geometric Brownian motion
........................185
4.2.3
Integrated Brownian motion
........................191
4.2.4
Brownian bridge
..................................^6
4.2.5
The Ornstein-Uhlenbeck process
....................1
4.2.6
The Bessel process
................................
204
4.3
White noise
.............................................
207
4.4
First-passage problems
...................................214
999
4.5
Exercises
...............................................
ΔΔΔ
5
Poisson
Processes
..........................................
zöí
5.1
The
Poisson
process
.....................................231
5.1.1
The telegraph signal
...............................
248
5.2
Nonhomogeneous
Poisson
processes
........................250
5.3
Compound
Poisson
processes
..............................254
5.4
Doubly stochastic
Poisson
processes
........................258
5.5
Filtered
Poisson
processes
................................264
5.6
Renewal processes
.......................................267
5.6.1
Limit theorems
....................................
2
°
5.6.2
Regenerative processes
.............................284
5.7
Exercises
...............................................289
6
Queueing Theory
..........................................
6.1
Introduction
............................................
31o
6.2
Queues with a single server
...............................319
6.2.1
The model M/M/l
................................
319
6.2.2
The model M/M/l/c
..............................
327
6.3
Queues with many servers
................................332
6.3.1
The model M/M/s
................................332
6.3.2
The model M/M/s/c and loss systems
...............336
6.3.3
Networks of queues
................................342
6.4
Exercises
...............................................346
Appendix A: Statistical Tables
.................................357
Appendix B: Answers to Even-Numbered Exercises
...........363
References
.....................................................375
Index
..........................................................377
|
| adam_txt |
Contents
Preface
.
vii
List of Tables
. xi
List of Figures
.xiii
1
Review of Probability Theory
. 1
1.1
Elementary probability
. 1
1.2
Random variables
. 8
1.3
Random vectors
. 21
1.4
Exercises
. 34
2
Stochastic Processes
. 47
2.1
Introduction and definitions
. 47
2.2
Stationarity
. 52
2.3
Ergodicity
. 55
2.4
Gaussian and Markovian processes
. 58
2.5
Exercises
. 65
3
Markov Chains
. 73
3.1
Introduction
. 73
3.2
Discrete-time Markov chains
. 77
3.2.1
Definitions and notations
. 77
3.2.2
Properties
. 85
3.2.3
Limiting probabilities
. 94
3.2.4
Absorption problems
.100
3.2.5
Branching processes
.104
3.3
Continuous-time Markov chains
.109
3.3.1
Exponential and gamma distributions
.109
3.3.2
Continuous-time Markov chains
.121
3.3.3
Calculation of the transition function Pij(t)
.124
x
Contents
3.3.4
Particular processes
.
129
3.3.5
Limiting probabilities
and balance
equations
.138
3.4
Exercises
.
143
4
Diffusion Processes
.
ί
'
°
4.1
The Wiener process
.
173
4.2
Diffusion processes
.
1°*
4.2.1
Brownian motion with drift
.
183
4.2.2
Geometric Brownian motion
.185
4.2.3
Integrated Brownian motion
.191
4.2.4
Brownian bridge
.^6
4.2.5
The Ornstein-Uhlenbeck process
.1"
4.2.6
The Bessel process
.
204
4.3
White noise
.
207
4.4
First-passage problems
.214
999
4.5
Exercises
.
ΔΔΔ
5
Poisson
Processes
.
zöí
5.1
The
Poisson
process
.231
5.1.1
The telegraph signal
.
248
5.2
Nonhomogeneous
Poisson
processes
.250
5.3
Compound
Poisson
processes
.254
5.4
Doubly stochastic
Poisson
processes
.258
5.5
Filtered
Poisson
processes
.264
5.6
Renewal processes
.267
5.6.1
Limit theorems
.
2
'
°
5.6.2
Regenerative processes
.284
5.7
Exercises
.289
6
Queueing Theory
.
6.1
Introduction
.
31o
6.2
Queues with a single server
.319
6.2.1
The model M/M/l
.
319
6.2.2
The model M/M/l/c
.
327
6.3
Queues with many servers
.332
6.3.1
The model M/M/s
.332
6.3.2
The model M/M/s/c and loss systems
.336
6.3.3
Networks of queues
.342
6.4
Exercises
.346
Appendix A: Statistical Tables
.357
Appendix B: Answers to Even-Numbered Exercises
.363
References
.375
Index
.377 |
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| genre_facet | Lehrbuch |
| id | DE-604.BV022444055 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T17:33:45Z |
| indexdate | 2024-07-09T20:57:43Z |
| institution | BVB |
| isbn | 0387341714 9780387341712 |
| language | English |
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| physical | X, 382 S. |
| publishDate | 2007 |
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| publisher | Springer |
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| spelling | Lefebvre, Mario 1957- Verfasser (DE-588)139314318 aut Applied stochastic processes Mario Lefebvre New York Springer 2007 X, 382 S. txt rdacontent n rdamedia nc rdacarrier Universitext Lehrbuch / Textbook - 28 Stochastischer Prozess / Theorie Stochastic processes Anwendung (DE-588)4196864-5 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Stochastische Resonanz (DE-588)4678002-6 gnd rswk-swf Stochastik (DE-588)4121729-9 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Stochastischer Prozess (DE-588)4057630-9 s Anwendung (DE-588)4196864-5 s DE-604 Stochastische Resonanz (DE-588)4678002-6 s Stochastik (DE-588)4121729-9 s 1\p DE-604 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015652055&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Lefebvre, Mario 1957- Applied stochastic processes Lehrbuch / Textbook - 28 Stochastischer Prozess / Theorie Stochastic processes Anwendung (DE-588)4196864-5 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Stochastische Resonanz (DE-588)4678002-6 gnd Stochastik (DE-588)4121729-9 gnd |
| subject_GND | (DE-588)4196864-5 (DE-588)4057630-9 (DE-588)4678002-6 (DE-588)4121729-9 (DE-588)4123623-3 |
| title | Applied stochastic processes |
| title_auth | Applied stochastic processes |
| title_exact_search | Applied stochastic processes |
| title_exact_search_txtP | Applied stochastic processes |
| title_full | Applied stochastic processes Mario Lefebvre |
| title_fullStr | Applied stochastic processes Mario Lefebvre |
| title_full_unstemmed | Applied stochastic processes Mario Lefebvre |
| title_short | Applied stochastic processes |
| title_sort | applied stochastic processes |
| topic | Lehrbuch / Textbook - 28 Stochastischer Prozess / Theorie Stochastic processes Anwendung (DE-588)4196864-5 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Stochastische Resonanz (DE-588)4678002-6 gnd Stochastik (DE-588)4121729-9 gnd |
| topic_facet | Lehrbuch / Textbook - 28 Stochastischer Prozess / Theorie Stochastic processes Anwendung Stochastischer Prozess Stochastische Resonanz Stochastik Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015652055&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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