Three classes of nonlinear stochastic partial differential equations:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
[Hackensack] New Jersey
World Scientific
[2013]
|
| Schlagwörter: | |
| Links: | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=592616 http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=592616 http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=592616 |
| Beschreibung: | Description based on print version record |
| Umfang: | 1 online resource (xi, 164 pages) |
| ISBN: | 1299651844 9781299651845 9789814452359 9789814452366 9814452351 981445236X |
Internformat
MARC
| LEADER | 00000nam a2200000zc 4500 | ||
|---|---|---|---|
| 001 | BV043035141 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 151120s2013 xx o|||| 00||| eng d | ||
| 020 | |a 1299651844 |c ebk |9 1-299-65184-4 | ||
| 020 | |a 9781299651845 |c ebk |9 978-1-299-65184-5 | ||
| 020 | |a 9789814452359 |9 978-981-4452-35-9 | ||
| 020 | |a 9789814452366 |c electronic bk. |9 978-981-4452-36-6 | ||
| 020 | |a 9814452351 |9 981-4452-35-1 | ||
| 020 | |a 981445236X |c electronic bk. |9 981-4452-36-X | ||
| 035 | |a (OCoLC)844311148 | ||
| 035 | |a (DE-599)BVBBV043035141 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-1046 |a DE-1047 | ||
| 082 | 0 | |a 519.2 |2 22 | |
| 100 | 1 | |a Xiong, Jie |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Three classes of nonlinear stochastic partial differential equations |c Jie Xiong |
| 264 | 1 | |a [Hackensack] New Jersey |b World Scientific |c [2013] | |
| 264 | 4 | |c © 2013 | |
| 300 | |a 1 online resource (xi, 164 pages) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 500 | |a Description based on print version record | ||
| 505 | 8 | |a The study of measure-valued processes in random environments has seen some intensive research activities in recent years whereby interesting nonlinear stochastic partial differential equations (SPDEs) were derived. Due to the nonlinearity and the non-Lipschitz continuity of their coefficients, new techniques and concepts have recently been developed for the study of such SPDEs. These include the conditional Laplace transform technique, the conditional mild solution, and the bridge between SPDEs and some kind of backward stochastic differential equations. This volume provides an introduction to these topics with the aim of attracting more researchers into this exciting and young area of research. It can be considered as the first book of its kind. The tools introduced and developed for the study of measure-valued processes in random environments can be used in a much broader area of nonlinear SPDEs | |
| 505 | 8 | |a 1. Introduction to superprocesses. 1.1. Branching particle system. 1.2. The log-Laplace equation. 1.3. The moment duality. 1.4. The SPDE for the density. 1.5. The SPDE for the distribution. 1.6. Historical remarks -- 2. Superprocesses in random environments. 2.1. Introduction and main result. 2.2. The moment duality. 2.3. Conditional martingale problem. 2.4. Historical remarks -- 3. Linear SPDE. 3.1. An equation on measure space. 3.2. A duality representation. 3.3. Two estimates. 3.4. Historical remarks -- 4. Particle representations for a class of nonlinear SPDEs. 4.1. Introduction. 4.2. Solution for the system. 4.3. A nonlinear SPDE. 4.4. Historical remarks -- 5. Stochastic log-Laplace equation. 5.1. Introduction. 5.2. Approximation and two estimates. 5.3. Existence and uniqueness. 5.4. Conditional log-Laplace transform. 5.5. Historical remarks -- 6. SPDEs for density fields of the superprocesses in random environment. 6.1. Introduction. 6.2. Derivation of SPDE. 6.3. A convolution representation. 6.4. An estimate in spatial increment. 6.5. Estimates in time increment. 6.6. Historical remarks -- 7. Backward doubly stochastic differential equations. 7.1. Introduction and basic definitions. 7.2. Itô-Pardoux-Peng formula. 7.3. Uniqueness of solution. 7.4. Historical remarks -- 8. From SPDE to BSDE. 8.1. The SPDE for the distribution. 8.2. Existence of solution to SPDE. 8.3. From BSDE to SPDE. 8.4. Uniqueness for SPDE. 8.5. Historical remarks | |
| 650 | 7 | |a MATHEMATICS / Probability & Statistics / General |2 bisacsh | |
| 650 | 7 | |a Differential equations, Nonlinear |2 fast | |
| 650 | 7 | |a Stochastic partial differential equations |2 fast | |
| 650 | 4 | |a Stochastic partial differential equations | |
| 650 | 4 | |a Differential equations, Nonlinear | |
| 650 | 0 | 7 | |a Stochastische nichtlineare Differentialgleichung |0 (DE-588)4592295-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Partielle Differentialgleichung |0 (DE-588)4044779-0 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Stochastische nichtlineare Differentialgleichung |0 (DE-588)4592295-0 |D s |
| 689 | 0 | 1 | |a Partielle Differentialgleichung |0 (DE-588)4044779-0 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Druck-Ausgabe |a Xiong, Jie |t Three classes of nonlinear stochastic partial differential equations |
| 856 | 4 | 0 | |u http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=592616 |x Aggregator |3 Volltext |
| 912 | |a ZDB-4-EBA | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-028459791 | |
| 966 | e | |u http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=592616 |l DE-1046 |p ZDB-4-EBA |q FAW_PDA_EBA |x Aggregator |3 Volltext | |
| 966 | e | |u http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=592616 |l DE-1047 |p ZDB-4-EBA |q FAW_PDA_EBA |x Aggregator |3 Volltext | |
Datensatz im Suchindex
| _version_ | 1818981115785904128 |
|---|---|
| any_adam_object | |
| author | Xiong, Jie |
| author_facet | Xiong, Jie |
| author_role | aut |
| author_sort | Xiong, Jie |
| author_variant | j x jx |
| building | Verbundindex |
| bvnumber | BV043035141 |
| collection | ZDB-4-EBA |
| contents | The study of measure-valued processes in random environments has seen some intensive research activities in recent years whereby interesting nonlinear stochastic partial differential equations (SPDEs) were derived. Due to the nonlinearity and the non-Lipschitz continuity of their coefficients, new techniques and concepts have recently been developed for the study of such SPDEs. These include the conditional Laplace transform technique, the conditional mild solution, and the bridge between SPDEs and some kind of backward stochastic differential equations. This volume provides an introduction to these topics with the aim of attracting more researchers into this exciting and young area of research. It can be considered as the first book of its kind. The tools introduced and developed for the study of measure-valued processes in random environments can be used in a much broader area of nonlinear SPDEs 1. Introduction to superprocesses. 1.1. Branching particle system. 1.2. The log-Laplace equation. 1.3. The moment duality. 1.4. The SPDE for the density. 1.5. The SPDE for the distribution. 1.6. Historical remarks -- 2. Superprocesses in random environments. 2.1. Introduction and main result. 2.2. The moment duality. 2.3. Conditional martingale problem. 2.4. Historical remarks -- 3. Linear SPDE. 3.1. An equation on measure space. 3.2. A duality representation. 3.3. Two estimates. 3.4. Historical remarks -- 4. Particle representations for a class of nonlinear SPDEs. 4.1. Introduction. 4.2. Solution for the system. 4.3. A nonlinear SPDE. 4.4. Historical remarks -- 5. Stochastic log-Laplace equation. 5.1. Introduction. 5.2. Approximation and two estimates. 5.3. Existence and uniqueness. 5.4. Conditional log-Laplace transform. 5.5. Historical remarks -- 6. SPDEs for density fields of the superprocesses in random environment. 6.1. Introduction. 6.2. Derivation of SPDE. 6.3. A convolution representation. 6.4. An estimate in spatial increment. 6.5. Estimates in time increment. 6.6. Historical remarks -- 7. Backward doubly stochastic differential equations. 7.1. Introduction and basic definitions. 7.2. Itô-Pardoux-Peng formula. 7.3. Uniqueness of solution. 7.4. Historical remarks -- 8. From SPDE to BSDE. 8.1. The SPDE for the distribution. 8.2. Existence of solution to SPDE. 8.3. From BSDE to SPDE. 8.4. Uniqueness for SPDE. 8.5. Historical remarks |
| ctrlnum | (OCoLC)844311148 (DE-599)BVBBV043035141 |
| 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 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>04928nam a2200565zc 4500</leader><controlfield tag="001">BV043035141</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">151120s2013 xx o|||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">1299651844</subfield><subfield code="c">ebk</subfield><subfield code="9">1-299-65184-4</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781299651845</subfield><subfield code="c">ebk</subfield><subfield code="9">978-1-299-65184-5</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9789814452359</subfield><subfield code="9">978-981-4452-35-9</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9789814452366</subfield><subfield code="c">electronic bk.</subfield><subfield code="9">978-981-4452-36-6</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9814452351</subfield><subfield code="9">981-4452-35-1</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">981445236X</subfield><subfield code="c">electronic bk.</subfield><subfield code="9">981-4452-36-X</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)844311148</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV043035141</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-1046</subfield><subfield code="a">DE-1047</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">519.2</subfield><subfield code="2">22</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Xiong, Jie</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Three classes of nonlinear stochastic partial differential equations</subfield><subfield code="c">Jie Xiong</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">[Hackensack] New Jersey</subfield><subfield code="b">World Scientific</subfield><subfield code="c">[2013]</subfield></datafield><datafield tag="264" ind1=" " ind2="4"><subfield code="c">© 2013</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (xi, 164 pages)</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">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Description based on print version record</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">The study of measure-valued processes in random environments has seen some intensive research activities in recent years whereby interesting nonlinear stochastic partial differential equations (SPDEs) were derived. Due to the nonlinearity and the non-Lipschitz continuity of their coefficients, new techniques and concepts have recently been developed for the study of such SPDEs. These include the conditional Laplace transform technique, the conditional mild solution, and the bridge between SPDEs and some kind of backward stochastic differential equations. This volume provides an introduction to these topics with the aim of attracting more researchers into this exciting and young area of research. It can be considered as the first book of its kind. The tools introduced and developed for the study of measure-valued processes in random environments can be used in a much broader area of nonlinear SPDEs</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">1. Introduction to superprocesses. 1.1. Branching particle system. 1.2. The log-Laplace equation. 1.3. The moment duality. 1.4. The SPDE for the density. 1.5. The SPDE for the distribution. 1.6. Historical remarks -- 2. Superprocesses in random environments. 2.1. Introduction and main result. 2.2. The moment duality. 2.3. Conditional martingale problem. 2.4. Historical remarks -- 3. Linear SPDE. 3.1. An equation on measure space. 3.2. A duality representation. 3.3. Two estimates. 3.4. Historical remarks -- 4. Particle representations for a class of nonlinear SPDEs. 4.1. Introduction. 4.2. Solution for the system. 4.3. A nonlinear SPDE. 4.4. Historical remarks -- 5. Stochastic log-Laplace equation. 5.1. Introduction. 5.2. Approximation and two estimates. 5.3. Existence and uniqueness. 5.4. Conditional log-Laplace transform. 5.5. Historical remarks -- 6. SPDEs for density fields of the superprocesses in random environment. 6.1. Introduction. 6.2. Derivation of SPDE. 6.3. A convolution representation. 6.4. An estimate in spatial increment. 6.5. Estimates in time increment. 6.6. Historical remarks -- 7. Backward doubly stochastic differential equations. 7.1. Introduction and basic definitions. 7.2. Itô-Pardoux-Peng formula. 7.3. Uniqueness of solution. 7.4. Historical remarks -- 8. From SPDE to BSDE. 8.1. The SPDE for the distribution. 8.2. Existence of solution to SPDE. 8.3. From BSDE to SPDE. 8.4. Uniqueness for SPDE. 8.5. Historical remarks</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS / Probability & Statistics / General</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Differential equations, Nonlinear</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Stochastic partial differential equations</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Stochastic partial differential equations</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Differential equations, Nonlinear</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Stochastische nichtlineare Differentialgleichung</subfield><subfield code="0">(DE-588)4592295-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Partielle Differentialgleichung</subfield><subfield code="0">(DE-588)4044779-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Stochastische nichtlineare Differentialgleichung</subfield><subfield code="0">(DE-588)4592295-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Partielle Differentialgleichung</subfield><subfield code="0">(DE-588)4044779-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druck-Ausgabe</subfield><subfield code="a">Xiong, Jie</subfield><subfield code="t">Three classes of nonlinear stochastic partial differential equations</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=592616</subfield><subfield code="x">Aggregator</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-4-EBA</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-028459791</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=592616</subfield><subfield code="l">DE-1046</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FAW_PDA_EBA</subfield><subfield code="x">Aggregator</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=592616</subfield><subfield code="l">DE-1047</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FAW_PDA_EBA</subfield><subfield code="x">Aggregator</subfield><subfield code="3">Volltext</subfield></datafield></record></collection> |
| id | DE-604.BV043035141 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T17:26:12Z |
| institution | BVB |
| isbn | 1299651844 9781299651845 9789814452359 9789814452366 9814452351 981445236X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028459791 |
| oclc_num | 844311148 |
| open_access_boolean | |
| owner | DE-1046 DE-1047 |
| owner_facet | DE-1046 DE-1047 |
| physical | 1 online resource (xi, 164 pages) |
| psigel | ZDB-4-EBA ZDB-4-EBA FAW_PDA_EBA |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Xiong, Jie Verfasser aut Three classes of nonlinear stochastic partial differential equations Jie Xiong [Hackensack] New Jersey World Scientific [2013] © 2013 1 online resource (xi, 164 pages) txt rdacontent c rdamedia cr rdacarrier Description based on print version record The study of measure-valued processes in random environments has seen some intensive research activities in recent years whereby interesting nonlinear stochastic partial differential equations (SPDEs) were derived. Due to the nonlinearity and the non-Lipschitz continuity of their coefficients, new techniques and concepts have recently been developed for the study of such SPDEs. These include the conditional Laplace transform technique, the conditional mild solution, and the bridge between SPDEs and some kind of backward stochastic differential equations. This volume provides an introduction to these topics with the aim of attracting more researchers into this exciting and young area of research. It can be considered as the first book of its kind. The tools introduced and developed for the study of measure-valued processes in random environments can be used in a much broader area of nonlinear SPDEs 1. Introduction to superprocesses. 1.1. Branching particle system. 1.2. The log-Laplace equation. 1.3. The moment duality. 1.4. The SPDE for the density. 1.5. The SPDE for the distribution. 1.6. Historical remarks -- 2. Superprocesses in random environments. 2.1. Introduction and main result. 2.2. The moment duality. 2.3. Conditional martingale problem. 2.4. Historical remarks -- 3. Linear SPDE. 3.1. An equation on measure space. 3.2. A duality representation. 3.3. Two estimates. 3.4. Historical remarks -- 4. Particle representations for a class of nonlinear SPDEs. 4.1. Introduction. 4.2. Solution for the system. 4.3. A nonlinear SPDE. 4.4. Historical remarks -- 5. Stochastic log-Laplace equation. 5.1. Introduction. 5.2. Approximation and two estimates. 5.3. Existence and uniqueness. 5.4. Conditional log-Laplace transform. 5.5. Historical remarks -- 6. SPDEs for density fields of the superprocesses in random environment. 6.1. Introduction. 6.2. Derivation of SPDE. 6.3. A convolution representation. 6.4. An estimate in spatial increment. 6.5. Estimates in time increment. 6.6. Historical remarks -- 7. Backward doubly stochastic differential equations. 7.1. Introduction and basic definitions. 7.2. Itô-Pardoux-Peng formula. 7.3. Uniqueness of solution. 7.4. Historical remarks -- 8. From SPDE to BSDE. 8.1. The SPDE for the distribution. 8.2. Existence of solution to SPDE. 8.3. From BSDE to SPDE. 8.4. Uniqueness for SPDE. 8.5. Historical remarks MATHEMATICS / Probability & Statistics / General bisacsh Differential equations, Nonlinear fast Stochastic partial differential equations fast Stochastic partial differential equations Differential equations, Nonlinear Stochastische nichtlineare Differentialgleichung (DE-588)4592295-0 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Stochastische nichtlineare Differentialgleichung (DE-588)4592295-0 s Partielle Differentialgleichung (DE-588)4044779-0 s 1\p DE-604 Erscheint auch als Druck-Ausgabe Xiong, Jie Three classes of nonlinear stochastic partial differential equations http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=592616 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Xiong, Jie Three classes of nonlinear stochastic partial differential equations The study of measure-valued processes in random environments has seen some intensive research activities in recent years whereby interesting nonlinear stochastic partial differential equations (SPDEs) were derived. Due to the nonlinearity and the non-Lipschitz continuity of their coefficients, new techniques and concepts have recently been developed for the study of such SPDEs. These include the conditional Laplace transform technique, the conditional mild solution, and the bridge between SPDEs and some kind of backward stochastic differential equations. This volume provides an introduction to these topics with the aim of attracting more researchers into this exciting and young area of research. It can be considered as the first book of its kind. The tools introduced and developed for the study of measure-valued processes in random environments can be used in a much broader area of nonlinear SPDEs 1. Introduction to superprocesses. 1.1. Branching particle system. 1.2. The log-Laplace equation. 1.3. The moment duality. 1.4. The SPDE for the density. 1.5. The SPDE for the distribution. 1.6. Historical remarks -- 2. Superprocesses in random environments. 2.1. Introduction and main result. 2.2. The moment duality. 2.3. Conditional martingale problem. 2.4. Historical remarks -- 3. Linear SPDE. 3.1. An equation on measure space. 3.2. A duality representation. 3.3. Two estimates. 3.4. Historical remarks -- 4. Particle representations for a class of nonlinear SPDEs. 4.1. Introduction. 4.2. Solution for the system. 4.3. A nonlinear SPDE. 4.4. Historical remarks -- 5. Stochastic log-Laplace equation. 5.1. Introduction. 5.2. Approximation and two estimates. 5.3. Existence and uniqueness. 5.4. Conditional log-Laplace transform. 5.5. Historical remarks -- 6. SPDEs for density fields of the superprocesses in random environment. 6.1. Introduction. 6.2. Derivation of SPDE. 6.3. A convolution representation. 6.4. An estimate in spatial increment. 6.5. Estimates in time increment. 6.6. Historical remarks -- 7. Backward doubly stochastic differential equations. 7.1. Introduction and basic definitions. 7.2. Itô-Pardoux-Peng formula. 7.3. Uniqueness of solution. 7.4. Historical remarks -- 8. From SPDE to BSDE. 8.1. The SPDE for the distribution. 8.2. Existence of solution to SPDE. 8.3. From BSDE to SPDE. 8.4. Uniqueness for SPDE. 8.5. Historical remarks MATHEMATICS / Probability & Statistics / General bisacsh Differential equations, Nonlinear fast Stochastic partial differential equations fast Stochastic partial differential equations Differential equations, Nonlinear Stochastische nichtlineare Differentialgleichung (DE-588)4592295-0 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| subject_GND | (DE-588)4592295-0 (DE-588)4044779-0 |
| title | Three classes of nonlinear stochastic partial differential equations |
| title_auth | Three classes of nonlinear stochastic partial differential equations |
| title_exact_search | Three classes of nonlinear stochastic partial differential equations |
| title_full | Three classes of nonlinear stochastic partial differential equations Jie Xiong |
| title_fullStr | Three classes of nonlinear stochastic partial differential equations Jie Xiong |
| title_full_unstemmed | Three classes of nonlinear stochastic partial differential equations Jie Xiong |
| title_short | Three classes of nonlinear stochastic partial differential equations |
| title_sort | three classes of nonlinear stochastic partial differential equations |
| topic | MATHEMATICS / Probability & Statistics / General bisacsh Differential equations, Nonlinear fast Stochastic partial differential equations fast Stochastic partial differential equations Differential equations, Nonlinear Stochastische nichtlineare Differentialgleichung (DE-588)4592295-0 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| topic_facet | MATHEMATICS / Probability & Statistics / General Differential equations, Nonlinear Stochastic partial differential equations Stochastische nichtlineare Differentialgleichung Partielle Differentialgleichung |
| url | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=592616 |
| work_keys_str_mv | AT xiongjie threeclassesofnonlinearstochasticpartialdifferentialequations |