Random processes by example
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New Jersey [u.a.]
World Scientific
2014
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV042141913 | ||
| 003 | DE-604 | ||
| 005 | 20160621 | ||
| 007 | t | ||
| 008 | 141023s2014 xxud||| |||| 00||| eng d | ||
| 010 | |a 013048543 | ||
| 020 | |a 9789814522281 |9 978-981-4522-28-1 | ||
| 035 | |a (OCoLC)896727055 | ||
| 035 | |a (DE-599)BVBBV042141913 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 044 | |a xxu |c US | ||
| 049 | |a DE-824 |a DE-11 |a DE-384 |a DE-83 | ||
| 050 | 0 | |a QA274 | |
| 082 | 0 | |a 519.2/3 |2 23 | |
| 084 | |a SK 820 |0 (DE-625)143258: |2 rvk | ||
| 084 | |a 60Gxx |2 msc | ||
| 100 | 1 | |a Lifšic, Michail A. |d 1956- |e Verfasser |0 (DE-588)12396718X |4 aut | |
| 245 | 1 | 0 | |a Random processes by example |c Mikhail Lifshits |
| 264 | 1 | |a New Jersey [u.a.] |b World Scientific |c 2014 | |
| 300 | |a XI, 219 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Stochastic processes |x Mathematical models | |
| 650 | 0 | 7 | |a Stochastischer Prozess |0 (DE-588)4057630-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mathematisches Modell |0 (DE-588)4114528-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mathematische Modellierung |0 (DE-588)7651795-0 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Stochastischer Prozess |0 (DE-588)4057630-9 |D s |
| 689 | 0 | 1 | |a Mathematisches Modell |0 (DE-588)4114528-8 |D s |
| 689 | 0 | 2 | |a Mathematische Modellierung |0 (DE-588)7651795-0 |D s |
| 689 | 0 | |5 DE-604 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027581874&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027581874 | ||
Datensatz im Suchindex
| _version_ | 1804152627496222720 |
|---|---|
| adam_text | Titel: Random processes by example
Autor: Lifšic, Michail A
Jahr: 2014
Contents
Preface v
Acknowledgments vii
1. Preliminaries 1
1 Random Variables: a Summary............... 1
1.1 Probability space, events, independence...... 1
1.2 Random variables and their distributions..... 3
1.3 Expectation..................... 6
1.4 Inequalities based on expectation......... 8
1.5 Variance....................... 9
1.6 Covariance, correlation coefficient......... 11
1.7 Complex-valued random variables......... 13
1.8 Characteristic functions............... 13
1.9 Convergence of random variables.......... 16
2 From Poisson to Stable Variables.............. 19
2.1 Compound Poisson variables............ 19
2.2 Limits of Compound Poisson variables....... 22
2.3 A mystery at zero.................. 26
2.4 Infinitely divisible random variables........ 27
2.5 Stable variables................... 28
3 Limit Theorems for Sums and Domains of Attraction ... 33
4 Random Vectors....................... 35
4.1 Definition....................... 35
4.2 Convergence of random vectors .......... 39
4.3 Gaussian vectors................... 41
4.4 Multivariate CLT.................. 45
x Contents
4.5 Stable vectors.................... 46
2. Random Processes 47
5 Random Processes: Main Classes.............. 47
6 Examples of Gaussian Random Processes......... 50
6.1 Wiener process.................... 51
6.2 Brownian bridge................... 55
6.3 Ornstein-Uhlenbeck process............ 58
6.4 Fractional Brownian motion............ 59
6.5 Brownian sheet ................... 63
6.6 Levy s Brownian function.............. 65
6.7 Further extensions.................. 65
7 Random Measures and Stochastic Integrals........ 67
7.1 Random measures with uncorrelated values .... 67
7.2 Gaussian white noise................ 71
7.3 Integral representations............... 73
7.4 Poisson random measures and integrals...... 78
7.5 Independently scattered stable random measures
and integrals..................... 87
8 Limit Theorems for Poisson Integrals............ 92
8.1 Convergence to the normal distribution...... 92
8.2 Convergence to a stable distribution........ 94
9 Levy Processes........................ 97
9.1 General Levy processes............... 97
9.2 Compound Poisson processes............ 101
9.3 Stable Levy processes................ 101
10 Spectral Representations................... 105
10.1 Wide sense stationary processes.......... 105
10.2 Spectral representations............... 106
10.3 Further extensions.................. 112
11 Convergence of Random Processes............. 114
11.1 Finite-dimensional convergence........... 114
11.2 Weak convergence.................. 118
3. Teletraffic Models 131
12 A Model of Service System ................. 132
12.1 Main assumptions on the service time and resource
consummation.................... 134
Contents xi
12.2 Analysis of workload variance........... 136
13 Limit Theorems for the Workload.............. 141
13.1 Centered and scaled workload process....... 141
13.2 Weak dependence: convergence to Wiener process 143
13.3 Long ränge dependence: convergence to fBm . . . 151
13.4 Convergence to a stable Levy process....... 157
13.5 Convergence to Telecom processes......... 172
13.6 Handling messengers from the past ....... 178
14 Micropulse Model....................... 180
15 Spacial Extensions...................... 188
15.1 Spacial model.................... 188
15.2 Spacial noise integrals................ 190
15.3 Limit theorems for spacial load........... 192
Notations 203
Bibliography 207
Index 215
|
| any_adam_object | 1 |
| author | Lifšic, Michail A. 1956- |
| author_GND | (DE-588)12396718X |
| author_facet | Lifšic, Michail A. 1956- |
| author_role | aut |
| author_sort | Lifšic, Michail A. 1956- |
| author_variant | m a l ma mal |
| building | Verbundindex |
| bvnumber | BV042141913 |
| callnumber-first | Q - Science |
| callnumber-label | QA274 |
| callnumber-raw | QA274 |
| callnumber-search | QA274 |
| callnumber-sort | QA 3274 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 820 |
| ctrlnum | (OCoLC)896727055 (DE-599)BVBBV042141913 |
| dewey-full | 519.2/3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2/3 |
| dewey-search | 519.2/3 |
| dewey-sort | 3519.2 13 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01775nam a2200457 c 4500</leader><controlfield tag="001">BV042141913</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20160621 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">141023s2014 xxud||| |||| 00||| eng d</controlfield><datafield tag="010" ind1=" " ind2=" "><subfield code="a">013048543</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9789814522281</subfield><subfield code="9">978-981-4522-28-1</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)896727055</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042141913</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">xxu</subfield><subfield code="c">US</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-824</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-384</subfield><subfield code="a">DE-83</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA274</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">519.2/3</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 820</subfield><subfield code="0">(DE-625)143258:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">60Gxx</subfield><subfield code="2">msc</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Lifšic, Michail A.</subfield><subfield code="d">1956-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)12396718X</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Random processes by example</subfield><subfield code="c">Mikhail Lifshits</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New Jersey [u.a.]</subfield><subfield code="b">World Scientific</subfield><subfield code="c">2014</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XI, 219 S.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references and index</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematisches Modell</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Stochastic processes</subfield><subfield code="x">Mathematical models</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Stochastischer Prozess</subfield><subfield code="0">(DE-588)4057630-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Mathematisches Modell</subfield><subfield code="0">(DE-588)4114528-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Mathematische Modellierung</subfield><subfield code="0">(DE-588)7651795-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Stochastischer Prozess</subfield><subfield code="0">(DE-588)4057630-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Mathematisches Modell</subfield><subfield code="0">(DE-588)4114528-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Mathematische Modellierung</subfield><subfield code="0">(DE-588)7651795-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027581874&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027581874</subfield></datafield></record></collection> |
| id | DE-604.BV042141913 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T01:13:43Z |
| institution | BVB |
| isbn | 9789814522281 |
| language | English |
| lccn | 013048543 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027581874 |
| oclc_num | 896727055 |
| open_access_boolean | |
| owner | DE-824 DE-11 DE-384 DE-83 |
| owner_facet | DE-824 DE-11 DE-384 DE-83 |
| physical | XI, 219 S. graph. Darst. |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Lifšic, Michail A. 1956- Verfasser (DE-588)12396718X aut Random processes by example Mikhail Lifshits New Jersey [u.a.] World Scientific 2014 XI, 219 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Mathematisches Modell Stochastic processes Mathematical models Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Mathematische Modellierung (DE-588)7651795-0 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 s Mathematisches Modell (DE-588)4114528-8 s Mathematische Modellierung (DE-588)7651795-0 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027581874&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lifšic, Michail A. 1956- Random processes by example Mathematisches Modell Stochastic processes Mathematical models Stochastischer Prozess (DE-588)4057630-9 gnd Mathematisches Modell (DE-588)4114528-8 gnd Mathematische Modellierung (DE-588)7651795-0 gnd |
| subject_GND | (DE-588)4057630-9 (DE-588)4114528-8 (DE-588)7651795-0 |
| title | Random processes by example |
| title_auth | Random processes by example |
| title_exact_search | Random processes by example |
| title_full | Random processes by example Mikhail Lifshits |
| title_fullStr | Random processes by example Mikhail Lifshits |
| title_full_unstemmed | Random processes by example Mikhail Lifshits |
| title_short | Random processes by example |
| title_sort | random processes by example |
| topic | Mathematisches Modell Stochastic processes Mathematical models Stochastischer Prozess (DE-588)4057630-9 gnd Mathematisches Modell (DE-588)4114528-8 gnd Mathematische Modellierung (DE-588)7651795-0 gnd |
| topic_facet | Mathematisches Modell Stochastic processes Mathematical models Stochastischer Prozess Mathematische Modellierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027581874&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT lifsicmichaila randomprocessesbyexample |