Three classes of nonlinear stochastic partial differential equations:
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| Format: | Electronic eBook |
| Language: | English |
| Published: |
[Hackensack] New Jersey
World Scientific
[2013]
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| Subjects: | |
| Online Access: | FAW01 FAW02 Volltext |
| Item Description: | Description based on print version record |
| Physical Description: | 1 online resource (xi, 164 pages) |
| ISBN: | 1299651844 9781299651845 9789814452359 9789814452366 9814452351 981445236X |
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| 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 | |
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| 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 | |
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| 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 |
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| id | DE-604.BV043035141 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:15:36Z |
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| isbn | 1299651844 9781299651845 9789814452359 9789814452366 9814452351 981445236X |
| language | English |
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| 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 |
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