Adventures in stochastic processes:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston, [u.a.]
Birkhäuser
[2002]
|
| Ausgabe: | Third printing |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverzeichnis Seite 613 - 616 |
| Beschreibung: | xii, 626 Seiten Illustrationen |
| ISBN: | 0817635912 3764335912 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV014804778 | ||
| 003 | DE-604 | ||
| 005 | 20241120 | ||
| 007 | t| | ||
| 008 | 021016s2002 xx a||| |||| 00||| eng d | ||
| 020 | |a 0817635912 |9 0-8176-3591-2 | ||
| 020 | |a 3764335912 |9 3-7643-3591-2 | ||
| 035 | |a (OCoLC)318261486 | ||
| 035 | |a (DE-599)BVBBV014804778 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-19 |a DE-91 |a DE-739 |a DE-91G |a DE-2070s |a DE-11 |a DE-188 | ||
| 082 | 0 | |a 519.2 | |
| 084 | |a QH 237 |0 (DE-625)141552: |2 rvk | ||
| 084 | |a SK 820 |0 (DE-625)143258: |2 rvk | ||
| 084 | |a 60Kxx |2 msc/2000 | ||
| 084 | |a MAT 605f |2 stub | ||
| 100 | 1 | |a Resnick, Sidney I. |d 1945- |0 (DE-588)111457114 |4 aut | |
| 245 | 1 | 0 | |a Adventures in stochastic processes |c Sidney Resnick |
| 250 | |a Third printing | ||
| 264 | 1 | |a Boston, [u.a.] |b Birkhäuser |c [2002] | |
| 264 | 4 | |c © 2002 | |
| 300 | |a xii, 626 Seiten |b Illustrationen | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Literaturverzeichnis Seite 613 - 616 | ||
| 650 | 4 | |a Procesos estocásticos | |
| 650 | 0 | 7 | |a Stochastischer Prozess |0 (DE-588)4057630-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Stochastischer Prozess |0 (DE-588)4057630-9 |D s |
| 689 | 0 | |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-1-4612-0387-2 |
| 856 | 4 | 2 | |m Digitalisierung UB Passau |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010019391&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-010019391 | |
Datensatz im Suchindex
| _version_ | 1816246552118689792 |
|---|---|
| adam_text |
Table
of
Contents
Preface
. ix
Chapter
1.
Preliminaries: Discrete Index Sets
and/or Discrete State Spaces
1.1.
Non-negative integer valued random variables
. 1
1.2.
Convolution
. 5
1.3.
Generating functions
. 7
1.3.1.
Differentiation of generating functions
. 9
1.3.2.
Generating functions and moments
. 10
1.3.3.
Generating functions and convolution
. 12
1.3.4.
Generating functions, compounding and random sums
. . 15
1.4.
The simple branching process
. . 18
1.5.
Limit distributions and the continuity theorem
. 27
1.5.1.
The law of rare events
. 30
1.6.
The simple random walk
. 33
1.7.
The distribution of a process*
. 40
1.8.
Stopping times*
. 44
1.8.1.
Wald's identity
. 47
1.8.2.
Splitting an iid sequence at a stopping time
* . 48
Exercises for Chapter
1. 51
Chapter
2.
Markov Chains
2.1.
Construction and first properties
. 61
2.2.
Examples
. 66
2.3.
Higher order transition probabilities
. 72
2.4.
Decomposition of the state space
. 77
2.5.
The dissection principle
. 81
2.6.
Transience and recurrence
. 85
2.7.
Periodicity
. 91
2.8.
Solidarity properties
. 92
2.9.
Examples
. 94
2.10.
Canonical decomposition
. 98
2.11.
Absorption probabilities
. 102
2.12.
Invariant measures and stationary distributions
.116
*This section contains advanced material which may be skipped on first read¬
ing by beginning readers.
vi
Contents
2.12.1.
Time averages
. 122
2.13.
Limit distributions
. 126
2.13.1
More on null recurrence and transience*
. . 134
2.14.
Computation of the stationary distribution
. 137
2.15.
Classification techniques
. 142
Exercises for Chapter
2. 147
Chapter
3.
Renewal Theory
3.1.
Basics
. 174
3.2.
Analytic interlude
. 176
3.2.1.
Integration
. 176
3.2.2.
Convolution
. 178
3.2.3.
Laplace transforms
. 181
3.3.
Counting renewals
. 185
3.4.
Renewal reward processes
. 192
3.5.
The renewal equation
. 197
3.5.1.
Risk processes*
. 205
3.6.
The
Poisson
process as a renewal process
. 211
3.7.
Informal discussion of renewal limit theorems;
regenerative processes
. 212
3.7.1
An informal discussion of regenerative processes
. 215
3.8.
Discrete renewal theory
. 221
3.9.
Stationary renewal processes*
. 224
3.10. Blackwell
and key renewal theorems*
. 230
3.10.1.
Direct Riemann integrability*
. . 231
3.10.2.
Equivalent forms of the renewal theorems*
. 237
3.10.3.
Proof of the renewal theorem*
. 243
3.11.
Improper renewal equations
. 253
3.12.
More regenerative processes*
. 259
3.12.1.
Definitions and examples*
. 259
3.12.2.
The renewal equation and Smith's theorem*
. 263
3.12.3.
Queueing examples
. 269
Exercises for Chapter
3. 280
Chapter
4.
Point Processes
4.1.
Basics
. 300
4.2.
The
Poisson
process
. 303
4.3.
Transforming
Poisson
processes
. 308
*This section contains advanced material which may be skipped on first read¬
ing by beginning readers.
Contents
vii
4.3.1.
Max-stable and stable
random variables*
. 313
4.4.
More transformation theory; marking and thinning
. 316
4.5.
The order statistic property
. 321
4.6.
Variants of the
Poisson
process
. 327
4.7.
Technical basics*
. 333
4.7.1.
The Laplace functional*
. 336
4.8.
More on the
Poisson
process*
. 337
4.9.
A general construction of the
Poisson
process;
a simple derivation of the order statistic property*
. 341
4.10.
More transformation theory; location dependent thinning*
. 343
4.11.
Records*
. 346
Exercises for Chapter
4. 349
Chapter
5.
Continuous Time Markov Chains
5.1.
Definitions and construction
. 367
5.2.
Stability and explosions
. 375
5.2.1.
The Markov property*
. 377
5.3.
Dissection
. 380
5.3.1.
More detail on dissection*
. 380
5.4.
The backward equation and the generator matrix
. 382
5.5.
Stationary and limiting distributions
. 392
5.5.1.
More on invariant measures*
. 398
5.6.
Laplace transform methods
. 402
5.7.
Calculations and examples
. 406
5.7.1.
Queueing networks
. 415
5.8.
Time dependent solutions*
. 426
5.9.
Reversibility
. 431
5.10.
Uniformizability
. 436
5.11.
The linear birth process as a point process
. 439
Exercises for Chapter
5. 446
Chapter
6.
Brownian Motion
6.1.
Introduction
. 482
6.2.
Preliminaries
. 487
6.3.
Construction of Brownian motion*
. 489
6.4.
Simple properties of standard Brownian motion
. 494
6.5.
The reflection principle and the distribution of the maximum
497
6.6.
The strong independent increment property and reflection*
. 504
6.7.
Escape from a strip
. 508
*This section contains advanced material which may be skipped on first read¬
ing by beginning readers.
viii
Contents
6.8.
Brownian
motion with drift
. 511
6.9.
Heavy traffic approximations in queueing theory
. 514
6.10.
The Brownian bridge and the Kolmogorov-Smirnov statistic
. 524
6.11.
Path properties*
. 539
6.12.
Quadratic variation
. 542
6.13.
Khintchine's law of the iterated logarithm for Brownian motion*
546
Exercises for Chapter
6. 551
Chapter
7.
The General Random Walk*
7.1.
Stopping times
. 559
7.2.
Global properties
. 561
7.3.
Prelude to
Wiener-Hopf:
Probabilistic interpretations
of transforms
. 564
7.4.
Dual pairs of stopping times
. 568
7.5. Wiener-Hopf
decompositions
. 573
7.6.
Consequences of the
Wiener-Hopf
factorization
. 581
7.7.
The maximum of a random walk
. 587
7.8.
Random walks and the G/G/l queue
. 591
7.8.1.
Exponential right tail
. 595
7.8.2.
Application to G/M/l queueing model
. 599
7.8.3.
Exponential left tail
. 602
7.8.4.
The M/G/l queue
. 605
7.8.5.
Queue lengths
. 607
References
. 613
Index
. 617
*This section contains advanced material which may be skipped on first read¬
ing by beginning readers. |
| any_adam_object | 1 |
| author | Resnick, Sidney I. 1945- |
| author_GND | (DE-588)111457114 |
| author_facet | Resnick, Sidney I. 1945- |
| author_role | aut |
| author_sort | Resnick, Sidney I. 1945- |
| author_variant | s i r si sir |
| building | Verbundindex |
| bvnumber | BV014804778 |
| classification_rvk | QH 237 SK 820 |
| classification_tum | MAT 605f |
| ctrlnum | (OCoLC)318261486 (DE-599)BVBBV014804778 |
| dewey-full | 519.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 |
| dewey-search | 519.2 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | Third printing |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>00000nam a2200000 c 4500</leader><controlfield tag="001">BV014804778</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20241120</controlfield><controlfield tag="007">t|</controlfield><controlfield tag="008">021016s2002 xx a||| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0817635912</subfield><subfield code="9">0-8176-3591-2</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3764335912</subfield><subfield code="9">3-7643-3591-2</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)318261486</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV014804778</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-19</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-2070s</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">519.2</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">QH 237</subfield><subfield code="0">(DE-625)141552:</subfield><subfield code="2">rvk</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">60Kxx</subfield><subfield code="2">msc/2000</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 605f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Resnick, Sidney I.</subfield><subfield code="d">1945-</subfield><subfield code="0">(DE-588)111457114</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Adventures in stochastic processes</subfield><subfield code="c">Sidney Resnick</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">Third printing</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Boston, [u.a.]</subfield><subfield code="b">Birkhäuser</subfield><subfield code="c">[2002]</subfield></datafield><datafield tag="264" ind1=" " ind2="4"><subfield code="c">© 2002</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">xii, 626 Seiten</subfield><subfield code="b">Illustrationen</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">Literaturverzeichnis Seite 613 - 616</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Procesos estocásticos</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="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=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Online-Ausgabe</subfield><subfield code="z">978-1-4612-0387-2</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Passau</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=010019391&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-010019391</subfield></datafield></record></collection> |
| id | DE-604.BV014804778 |
| illustrated | Illustrated |
| indexdate | 2024-11-20T13:01:28Z |
| institution | BVB |
| isbn | 0817635912 3764335912 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010019391 |
| oclc_num | 318261486 |
| open_access_boolean | |
| owner | DE-19 DE-BY-UBM DE-91 DE-BY-TUM DE-739 DE-91G DE-BY-TUM DE-2070s DE-11 DE-188 |
| owner_facet | DE-19 DE-BY-UBM DE-91 DE-BY-TUM DE-739 DE-91G DE-BY-TUM DE-2070s DE-11 DE-188 |
| physical | xii, 626 Seiten Illustrationen |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Birkhäuser |
| record_format | marc |
| spelling | Resnick, Sidney I. 1945- (DE-588)111457114 aut Adventures in stochastic processes Sidney Resnick Third printing Boston, [u.a.] Birkhäuser [2002] © 2002 xii, 626 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Literaturverzeichnis Seite 613 - 616 Procesos estocásticos Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4612-0387-2 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010019391&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Resnick, Sidney I. 1945- Adventures in stochastic processes Procesos estocásticos Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4057630-9 |
| title | Adventures in stochastic processes |
| title_auth | Adventures in stochastic processes |
| title_exact_search | Adventures in stochastic processes |
| title_full | Adventures in stochastic processes Sidney Resnick |
| title_fullStr | Adventures in stochastic processes Sidney Resnick |
| title_full_unstemmed | Adventures in stochastic processes Sidney Resnick |
| title_short | Adventures in stochastic processes |
| title_sort | adventures in stochastic processes |
| topic | Procesos estocásticos Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Procesos estocásticos Stochastischer Prozess |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010019391&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT resnicksidneyi adventuresinstochasticprocesses |