Simulation and chaotic behavior of alpha-stable stochastic processes:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Dekker
1994
|
| Schriftenreihe: | Pure and applied mathematics
178 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VII, 355 S. graph. Darst. |
| ISBN: | 0824788826 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV008883565 | ||
| 003 | DE-604 | ||
| 005 | 20150314 | ||
| 007 | t | ||
| 008 | 940214s1994 xxud||| |||| 00||| eng d | ||
| 020 | |a 0824788826 |9 0-8247-8882-6 | ||
| 035 | |a (OCoLC)246623665 | ||
| 035 | |a (DE-599)BVBBV008883565 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 044 | |a xxu |c XD-US | ||
| 049 | |a DE-384 |a DE-824 |a DE-29T |a DE-12 |a DE-739 |a DE-91G |a DE-703 |a DE-521 |a DE-634 |a DE-11 | ||
| 050 | 0 | |a QA274.J35 1994 | |
| 082 | 0 | |a 003.76 | |
| 082 | 0 | |a 003/.76 20 | |
| 084 | |a SK 820 |0 (DE-625)143258: |2 rvk | ||
| 084 | |a MAT 605f |2 stub | ||
| 100 | 1 | |a Janicki, Aleksander |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Simulation and chaotic behavior of alpha-stable stochastic processes |c Aleksander Janicki ; Aleksander Weron |
| 264 | 1 | |a New York [u.a.] |b Dekker |c 1994 | |
| 300 | |a VII, 355 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Pure and applied mathematics |v 178 | |
| 650 | 4 | |a Datenverarbeitung | |
| 650 | 4 | |a Stochastic processes -- Data processing | |
| 650 | 0 | 7 | |a Stochastischer Prozess |0 (DE-588)4057630-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Stabilität |0 (DE-588)4056693-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Computersimulation |0 (DE-588)4148259-1 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Stochastischer Prozess |0 (DE-588)4057630-9 |D s |
| 689 | 0 | 1 | |a Stabilität |0 (DE-588)4056693-6 |D s |
| 689 | 0 | 2 | |a Computersimulation |0 (DE-588)4148259-1 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Weron, Aleksander |e Verfasser |4 aut | |
| 830 | 0 | |a Pure and applied mathematics |v 178 |w (DE-604)BV000001885 |9 178 | |
| 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=005876664&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 940 | 1 | |n oe | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-005876664 | ||
Datensatz im Suchindex
| _version_ | 1804123240381022208 |
|---|---|
| adam_text | Contents
Preface iii
1 Preliminary Remarks 1
1.1 Historical Overview 1
1.2 Stochastic a Stable Modeling 3
1.3 Statistical versus Stochastic Modeling 4
1.4 Hierarchy of Chaos 6
1.5 Computer Simulations and Visualizations 6
1.6 Stochastic Processes 7
2 Brownian Motion, Poisson Process, a—Stable Levy Motion 9
2.1 Introduction 9
2.2 Brownian Motion 9
2.3 The Poisson Process 20
2.4 a Stable Random Variables 23
2.5 a Stable Levy Motion 30
3 Computer Simulation of a—Stable Random Variables 35
3.1 Introduction 35
3.2 Computer Methods of Generation of Random Variables 36
3.3 Series Representations of Stable Random Variables 40
3.4 Convergence of LePage Random Series 43
3.5 Computer Generation of a Stable Distributions 47
3.6 Exact Formula for Tail Probabilities 51
3.7 Density Estimators 55
4 Stochastic Integration 67
4.1 Introduction 67
4.2 Ito Stochastic Integral 69
4.3 a Stable Stochastic Integrals of Deterministic Functions .... 73
4.4 Infinitely Divisible Processes 75
4.5 Stochastic Integrals with ID Integrators 79
4.6 Levy Characteristics 83
4.7 Stochastic Processes as Integrators 86
4.8 Integrals of Deterministic Functions with ID Integrators 90
4.9 Integrals with Stochastic Integrands and ID Integrators 96
v
vi PREFACE
4.10 Diffusions Driven by Brownian Motion 101
4.11 Diffusions Driven by a Stable Levy Motion 107
5 Spectral Representations of Stationary Processes 111
5.1 Introduction HI
5.2 Gaussian Stationary Processes 112
5.3 Representation of a Stable Stochastic Processes 116
5.4 Structure of Stationary Stable Processes 127
5.5 Self similar a Stable Processes 134
6 Computer Approximations of Continuous Time Processes 141
6.1 Introduction 141
6.2 Approximation of Diffusions Driven by Brownian Motion . . . 142
6.3 Approximation of Diffusions Driven by a Stable Levy Measure . 156
6.4 Examples of Application in Mathematics 158
7 Examples of a Stable Stochastic Modeling 171
7.1 Survey of a Stable Modeling 171
7.2 Chaos, Levy Flight, and Levy Walk 173
7.3 Examples of Diffusions in Physics 179
7.4 Logistic Model of Population Growth 192
7.5 Option Pricing Model in Financial Economics 196
8 Convergence of Approximate Methods 203
8.1 Introduction 203
8.2 Error of Approximation of Ito Integrals 205
8.3 The Rate of Convergence of LePage Type Series 208
8.4 Approximation of Levy a Stable Diffusions 217
8.5 Applications to Statistical Tests of Hypotheses 218
8.6 Levy Processes and Poisson Random Measures 224
8.7 Limit Theorems for Sums of i.i.d. Random Variables 226
9 Chaotic Behavior of Stationary Processes 231
9.1 Examples of Chaotic Behavior 231
9.2 Ergodic Property of Stationary Gaussian Processes 239
9.3 Basic Facts of General Ergodic Theory 242
9.4 Birkhoff Theorem for Stationary Processes 246
9.5 Hierarchy of Chaotic Properties 251
9.6 Dynamical Functional 255
10 Hierarchy of Chaos for Stable and ID Stationary Processes 263
10.1 Introduction 263
10.2 Ergodicity of Stable Processes 265
10.3 Mixing and Other Chaotic Properties of Stable Processes .... 279
10.4 Introduction to Stationary ID Processes 287
10.5 Ergodic Properties of ID Processes 295
A. JANICKI and A. WERON vii
10.6 Mixing Properties of ID Processes 297
10.7 Examples of Chaotic Behavior of ID Processes 302
10.8 Random Measures on Sequences of Sets 307
Appendix: A Guide to Simulation 315
Bibliography 339
Index 353
|
| any_adam_object | 1 |
| author | Janicki, Aleksander Weron, Aleksander |
| author_facet | Janicki, Aleksander Weron, Aleksander |
| author_role | aut aut |
| author_sort | Janicki, Aleksander |
| author_variant | a j aj a w aw |
| building | Verbundindex |
| bvnumber | BV008883565 |
| callnumber-first | Q - Science |
| callnumber-label | QA274 |
| callnumber-raw | QA274.J35 1994 |
| callnumber-search | QA274.J35 1994 |
| callnumber-sort | QA 3274 J35 41994 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 820 |
| classification_tum | MAT 605f |
| ctrlnum | (OCoLC)246623665 (DE-599)BVBBV008883565 |
| dewey-full | 003.76 003/.7620 |
| dewey-hundreds | 000 - Computer science, information, general works |
| dewey-ones | 003 - Systems |
| dewey-raw | 003.76 003/.76 20 |
| dewey-search | 003.76 003/.76 20 |
| dewey-sort | 13.76 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Informatik Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01946nam a2200493 cb4500</leader><controlfield tag="001">BV008883565</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20150314 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">940214s1994 xxud||| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0824788826</subfield><subfield code="9">0-8247-8882-6</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)246623665</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV008883565</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</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">XD-US</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-12</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-521</subfield><subfield code="a">DE-634</subfield><subfield code="a">DE-11</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA274.J35 1994</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">003.76</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">003/.76 20</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">MAT 605f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Janicki, Aleksander</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Simulation and chaotic behavior of alpha-stable stochastic processes</subfield><subfield code="c">Aleksander Janicki ; Aleksander Weron</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New York [u.a.]</subfield><subfield code="b">Dekker</subfield><subfield code="c">1994</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">VII, 355 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="490" ind1="1" ind2=" "><subfield code="a">Pure and applied mathematics</subfield><subfield code="v">178</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Datenverarbeitung</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Stochastic processes -- Data processing</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">Stabilität</subfield><subfield code="0">(DE-588)4056693-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Computersimulation</subfield><subfield code="0">(DE-588)4148259-1</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">Stabilität</subfield><subfield code="0">(DE-588)4056693-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Computersimulation</subfield><subfield code="0">(DE-588)4148259-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Weron, Aleksander</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Pure and applied mathematics</subfield><subfield code="v">178</subfield><subfield code="w">(DE-604)BV000001885</subfield><subfield code="9">178</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=005876664&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="n">oe</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-005876664</subfield></datafield></record></collection> |
| id | DE-604.BV008883565 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:26:37Z |
| institution | BVB |
| isbn | 0824788826 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005876664 |
| oclc_num | 246623665 |
| open_access_boolean | |
| owner | DE-384 DE-824 DE-29T DE-12 DE-739 DE-91G DE-BY-TUM DE-703 DE-521 DE-634 DE-11 |
| owner_facet | DE-384 DE-824 DE-29T DE-12 DE-739 DE-91G DE-BY-TUM DE-703 DE-521 DE-634 DE-11 |
| physical | VII, 355 S. graph. Darst. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Dekker |
| record_format | marc |
| series | Pure and applied mathematics |
| series2 | Pure and applied mathematics |
| spelling | Janicki, Aleksander Verfasser aut Simulation and chaotic behavior of alpha-stable stochastic processes Aleksander Janicki ; Aleksander Weron New York [u.a.] Dekker 1994 VII, 355 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics 178 Datenverarbeitung Stochastic processes -- Data processing Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Stabilität (DE-588)4056693-6 gnd rswk-swf Computersimulation (DE-588)4148259-1 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 s Stabilität (DE-588)4056693-6 s Computersimulation (DE-588)4148259-1 s DE-604 Weron, Aleksander Verfasser aut Pure and applied mathematics 178 (DE-604)BV000001885 178 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005876664&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Janicki, Aleksander Weron, Aleksander Simulation and chaotic behavior of alpha-stable stochastic processes Pure and applied mathematics Datenverarbeitung Stochastic processes -- Data processing Stochastischer Prozess (DE-588)4057630-9 gnd Stabilität (DE-588)4056693-6 gnd Computersimulation (DE-588)4148259-1 gnd |
| subject_GND | (DE-588)4057630-9 (DE-588)4056693-6 (DE-588)4148259-1 |
| title | Simulation and chaotic behavior of alpha-stable stochastic processes |
| title_auth | Simulation and chaotic behavior of alpha-stable stochastic processes |
| title_exact_search | Simulation and chaotic behavior of alpha-stable stochastic processes |
| title_full | Simulation and chaotic behavior of alpha-stable stochastic processes Aleksander Janicki ; Aleksander Weron |
| title_fullStr | Simulation and chaotic behavior of alpha-stable stochastic processes Aleksander Janicki ; Aleksander Weron |
| title_full_unstemmed | Simulation and chaotic behavior of alpha-stable stochastic processes Aleksander Janicki ; Aleksander Weron |
| title_short | Simulation and chaotic behavior of alpha-stable stochastic processes |
| title_sort | simulation and chaotic behavior of alpha stable stochastic processes |
| topic | Datenverarbeitung Stochastic processes -- Data processing Stochastischer Prozess (DE-588)4057630-9 gnd Stabilität (DE-588)4056693-6 gnd Computersimulation (DE-588)4148259-1 gnd |
| topic_facet | Datenverarbeitung Stochastic processes -- Data processing Stochastischer Prozess Stabilität Computersimulation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005876664&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000001885 |
| work_keys_str_mv | AT janickialeksander simulationandchaoticbehaviorofalphastablestochasticprocesses AT weronaleksander simulationandchaoticbehaviorofalphastablestochasticprocesses |