Stochastic partial differential equations: a modeling, white noise functional approach
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
New York, NY [u.a.]
Springer
2010
|
| Edition: | 2. ed. |
| Series: | Universitext
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 304 S. graph. Darst. |
| ISBN: | 9780387894874 |
Staff View
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV035607198 | ||
| 003 | DE-604 | ||
| 005 | 20120718 | ||
| 007 | t | ||
| 008 | 090708s2010 gw d||| |||| 00||| eng d | ||
| 020 | |a 9780387894874 |9 978-0-387-89487-4 | ||
| 035 | |a (OCoLC)320493973 | ||
| 035 | |a (DE-599)BVBBV035607198 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 044 | |a gw |c DE | ||
| 049 | |a DE-20 |a DE-384 |a DE-824 |a DE-11 |a DE-188 |a DE-83 | ||
| 050 | 0 | |a QA274.25 | |
| 082 | 0 | |a 519.22 |2 22 | |
| 084 | |a QH 237 |0 (DE-625)141552: |2 rvk | ||
| 084 | |a SK 820 |0 (DE-625)143258: |2 rvk | ||
| 084 | |a MAT 606f |2 stub | ||
| 084 | |a 60J60 |2 msc | ||
| 084 | |a 35R60 |2 msc | ||
| 084 | |a 60H40 |2 msc | ||
| 084 | |a 60J75 |2 msc | ||
| 084 | |a 60H15 |2 msc | ||
| 245 | 1 | 0 | |a Stochastic partial differential equations |b a modeling, white noise functional approach |c Helge Holden ... |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York, NY [u.a.] |b Springer |c 2010 | |
| 300 | |a XV, 304 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Universitext | |
| 650 | 4 | |a Stochastic partial differential equations | |
| 650 | 0 | 7 | |a Stochastische partielle Differentialgleichung |0 (DE-588)4135969-0 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Stochastische partielle Differentialgleichung |0 (DE-588)4135969-0 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Holden, Helge |d 1956- |e Sonstige |0 (DE-588)111693667 |4 oth | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-0-387-89488-1 |
| 856 | 4 | 2 | |m OEBV Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017662397&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-017662397 | ||
Record in the Search Index
| _version_ | 1804139276979404800 |
|---|---|
| adam_text | CONTENTS PROFACE TO THE SECOND EDITION IX PREFACE TO THE FIRST EDITION
XI 1 INTRODUCTION 1 1.1 MODELING BY STOCHASTIC DIFFERENTIAL EQUATIONS 1
2 FRAMEWORK 13 2.1 WLIITE NOISE 13 2.1.1 THE 1-DIMENSIONAI, D-PARAMETER
SMOOTHED WHITE NOISE 13 2.1.2 THE (SMOOTHED) WHITE NOISE VECTOR 20 2.2
THE WIENER ITOE CHAOS EXPANSION 21 2.2.1 CHAOS EXPANSION IN TERMS OF
HERMITE POLYNOMIALS ... 21 2.2.2 CHAOS EXPANSION IN TERMS OF MULTIPLE
ITOE INTEGRALS... 29 2.3 THE HIDA STOCHASTIC TEST FUNCTIONS AND
STOCHASTIC DISTRIBUTIONS. THE KONDRATIEV SPACES {S)* :N , {S)*F 31 2.3.1
THE HIDA TEST FUNCTION SPACE (S) AND THE HIDA DISTRIBUTION SPACE (S)* 40
2.3.2 SINGULAR WHITE NOISE 42 2.4 THE WICK PRODUCT 43 2.4.1 SOME
EXAMPSES AND COUNTEREXAMPLES 47 2.5 WICK MULTIPLICATION AND
HITSUDA/SKOROHOD INTEGRATION 50 2.6 THE HERMITE TRANSFORM 61 2.7 THE
(S)^ R SPACES AND THE S- TRANSFORM 75 2.8 THE TOPOLOGY OF (5)UEF, 81 2.9
THE JF-TRANSFORM AND THE WICK PRODUCT ON L L {P) 88 2.10 THE WICK
PRODUCT AND TRANSLATION 92 2.11 POSITIVITV 98 XIV CONTENTS 3
APPLICATIONS TO STOCHASTIC ORDINARY DIFFERENTIAL EQUATIONS 115 3.1
LINEAR EQUATIONS 115 3.1.1 LINEAR 1-DIMENSIONAL EQUATIONS 115 3.1.2
SOINE REMARKS ON NUMERICAL SIMULATIONS 118 3.1.3 SONIC LINEAR
MULTIDIMENSIONAL EQUATIONS 119 3.2 A MODEL FOR POPULATION GROWTH IN A
CROWDED, STOCHASTIC ENVIRONMENT 120 3.2.1 THE GENERAL (S)_I SOLUTION 121
3.2.2 A SOLUTION IN L 1 ^) 123 3.2.3 A COMPARISON OF MODEL A AND MODEL B
127 3.3 A GENERAL EXISTENCE AND UNIQUENESS THEOREM 128 3-4 THE
STOCHASTIC VOLTERRA EQUATION 131 3-5 WICK PRODNCTS VERSUS ORDINARY
PRODUCTS: A COMPARISON EXPERIMENT 140 3.5.1 VARIANCE PROPERTICS 143 3.6
SOFUTION AND WICK APPROXIMATION OF QUASILINEAR SDE 145 3.7 USING WHITE
NOISE ANALYSIS TO SOLVE GENERAL NONLINEAR SDES 150 4 STOCHASTIC PARTIAL
DIFFERENTIAL EQUATIONS DRIVEN BY BROWNIAN WHITE NOISE 159 4.1 GENERAL
REMARKS 159 4.2 THE STOCHASTIC POISSON EQUATION 161 4.2.1 THE FUNCTIONAL
PROCESS APPROACH 163 4.3 THE STOCHASTIC TRANSPORT EQUATION 164 4.3.1
POLLUTION IN A TURBULENT MEDIUM 164 4.3.2 THE HEAT EQUATION WITH A
STOCHASTIE POTENTIAL 169 4.4 THE STOCHASTIC SCHROEDINGER EQUATION 169
4.4.1 /^(/O-PROPERTIES OF THE SOLUTION 172 4.5 THE VISCOUS BURGERS
EQUATION WITH A STOCHASTIC SOURCE 178 4.6 THE STOCHASTIC PRESSURE
EQUATION 186 4.6.1 THE SMOOTHED POSITIVE NOISE CASE 187 4.6.2 AN
INDUCTIVE APPROXIMATION PROCEDURE 192 4.6.3 THE 1-DIMENSIONAL CASC 193
4.G.4 THE SINGULAR POSITIVE NOISE CASE 194 4.7 THE HEAT EQUATION IN A
STOCHASTIC. ANISOTROPIE MEDIUM .... 195 4.8 A CLASS OF QUASILINEAR
PARABOLIC SPDES 200 4.9 SPDES DRIVEN BY POISSONIAN NOISE 203 5
STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS DRIVEN BY LEVY PROCESSES 213
5.1 INTRODUCTION 213 5.2 THE WHITE NOISE PROBABIUETY SPACE OF A LEVY
PROCESS (D = 1) 215 5.3 WHITE NOISE THEORY FOR A LEVY PROCESS (D * 1)
219 CONTENTS XV 5.3.1 CHAOS EXPANSION THEOREMS 219 .5.3.2 THE LEVY-HIDA-
KONDRATIEV SPACES 225 5.4 WHITE NOISE THEORY FOR A LEVY FIELD (D 1)
232 5.4.1 CONSTRUCTION OF THE LEVY FIELD 232 5.4.2 CHAOS EXPANSIONS AND
SKOROHOD INTEGRALS (D 1) .... 238 5.4.3 THE WIC K PRODUCT 244 5.4.4
THE HERMITE TRANSFORM 24F 5.5 THE STOCHASTIC POISSON EQUATION 248 5.6
WAVES IN A REGION WITH A LEVY WHITE NOISE FORCE 252 5.7 HEAT PROPAGATION
IN A DOMAIN WITH A LEVY WHITE NOISE POTENTIAL 253 APPENDIX A 257
APPENDIX B 203 APPENDIX C 271 APPENDIX D 273 APPENDIX E 281 REFERENCES
289 LIST OF FREQUENTLY USED NOTATIOII AND SYMBOLS 297 INDEX 303
|
| any_adam_object | 1 |
| author_GND | (DE-588)111693667 |
| building | Verbundindex |
| bvnumber | BV035607198 |
| callnumber-first | Q - Science |
| callnumber-label | QA274 |
| callnumber-raw | QA274.25 |
| callnumber-search | QA274.25 |
| callnumber-sort | QA 3274.25 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | QH 237 SK 820 |
| classification_tum | MAT 606f |
| ctrlnum | (OCoLC)320493973 (DE-599)BVBBV035607198 |
| dewey-full | 519.22 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.22 |
| dewey-search | 519.22 |
| dewey-sort | 3519.22 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 2. ed. |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01791nam a2200481 c 4500</leader><controlfield tag="001">BV035607198</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20120718 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">090708s2010 gw d||| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780387894874</subfield><subfield code="9">978-0-387-89487-4</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)320493973</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV035607198</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">gw</subfield><subfield code="c">DE</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-20</subfield><subfield code="a">DE-384</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield><subfield code="a">DE-83</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA274.25</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">519.22</subfield><subfield code="2">22</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">MAT 606f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">60J60</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">35R60</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">60H40</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">60J75</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">60H15</subfield><subfield code="2">msc</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Stochastic partial differential equations</subfield><subfield code="b">a modeling, white noise functional approach</subfield><subfield code="c">Helge Holden ...</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">2. ed.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New York, NY [u.a.]</subfield><subfield code="b">Springer</subfield><subfield code="c">2010</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XV, 304 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="0" ind2=" "><subfield code="a">Universitext</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Stochastic partial differential equations</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Stochastische partielle Differentialgleichung</subfield><subfield code="0">(DE-588)4135969-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Stochastische partielle Differentialgleichung</subfield><subfield code="0">(DE-588)4135969-0</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">Holden, Helge</subfield><subfield code="d">1956-</subfield><subfield code="e">Sonstige</subfield><subfield code="0">(DE-588)111693667</subfield><subfield code="4">oth</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">978-0-387-89488-1</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">OEBV 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=017662397&sequence=000001&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:BVB01-017662397</subfield></datafield></record></collection> |
| id | DE-604.BV035607198 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:41:31Z |
| institution | BVB |
| isbn | 9780387894874 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017662397 |
| oclc_num | 320493973 |
| open_access_boolean | |
| owner | DE-20 DE-384 DE-824 DE-11 DE-188 DE-83 |
| owner_facet | DE-20 DE-384 DE-824 DE-11 DE-188 DE-83 |
| physical | XV, 304 S. graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Springer |
| record_format | marc |
| series2 | Universitext |
| spelling | Stochastic partial differential equations a modeling, white noise functional approach Helge Holden ... 2. ed. New York, NY [u.a.] Springer 2010 XV, 304 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Universitext Stochastic partial differential equations Stochastische partielle Differentialgleichung (DE-588)4135969-0 gnd rswk-swf Stochastische partielle Differentialgleichung (DE-588)4135969-0 s DE-604 Holden, Helge 1956- Sonstige (DE-588)111693667 oth Erscheint auch als Online-Ausgabe 978-0-387-89488-1 OEBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017662397&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Stochastic partial differential equations a modeling, white noise functional approach Stochastic partial differential equations Stochastische partielle Differentialgleichung (DE-588)4135969-0 gnd |
| subject_GND | (DE-588)4135969-0 |
| title | Stochastic partial differential equations a modeling, white noise functional approach |
| title_auth | Stochastic partial differential equations a modeling, white noise functional approach |
| title_exact_search | Stochastic partial differential equations a modeling, white noise functional approach |
| title_full | Stochastic partial differential equations a modeling, white noise functional approach Helge Holden ... |
| title_fullStr | Stochastic partial differential equations a modeling, white noise functional approach Helge Holden ... |
| title_full_unstemmed | Stochastic partial differential equations a modeling, white noise functional approach Helge Holden ... |
| title_short | Stochastic partial differential equations |
| title_sort | stochastic partial differential equations a modeling white noise functional approach |
| title_sub | a modeling, white noise functional approach |
| topic | Stochastic partial differential equations Stochastische partielle Differentialgleichung (DE-588)4135969-0 gnd |
| topic_facet | Stochastic partial differential equations Stochastische partielle Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017662397&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT holdenhelge stochasticpartialdifferentialequationsamodelingwhitenoisefunctionalapproach |