Harnack Inequalities for Stochastic Partial Differential Equations (eBook, 2013) [WorldCat.org]
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Harnack Inequalities for Stochastic Partial Differential Equations
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Harnack Inequalities for Stochastic Partial Differential Equations

Author: Feng-Yu Wang
Publisher: New York, NY : Springer New York : Imprint: Springer, 2013.
Series: SpringerBriefs in mathematics
Edition/Format:   eBook : Document : English : 1st ed. 2013View all editions and formats
Summary:
In this book the author presents a self-contained account of Harnack inequalities and applications for the semigroup of solutions to stochastic partial and delayed differential equations. Since the semigroup refers to Fokker-Planck equations on infinite-dimensional spaces, the Harnack inequalities the author investigates are dimension-free. This is an essentially different point from the above mentioned classical  Read more...
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Material Type: Document
Document Type: Book, Computer File
All Authors / Contributors: Feng-Yu Wang
ISBN: 1461479347 9781461479345
OCLC Number: 1144422300
Language Note: English.
Notes: Description based upon print version of record.
Description: 1 online resource (135 p.).
Contents: ""Preface""; ""Contents""; ""Chapter 1 A General Theory of Dimension-Free Harnack Inequalities""; ""1.1 Coupling by Change of Measure and Applications""; ""1.1.1 Harnack Inequalities and Bismut Derivative Formulas""; ""1.1.2 Shift Harnack Inequalities and Integration by PartsFormulas""; ""1.2 Derivative Formulas Using the Malliavin Calculus""; ""1.2.1 Bismut Formulas""; ""1.2.2 Integration by Parts Formulas""; ""1.3 Harnack Inequalities and Gradient Inequalities""; ""1.3.1 Gradient�Entropy and Harnack Inequalities""; ""1.3.2 From Gradient�Gradient to Harnack Inequalities"" ""1.3.3 L2 Gradient and Harnack Inequalities""""1.4 Applications of Harnack and Shift Harnack Inequalities""; ""1.4.1 Applications of the Harnack Inequality""; ""1.4.2 Applications of the Shift Harnack Inequality""; ""Chapter 2 Nonlinear Monotone Stochastic Partial Differential Equations""; ""2.1 Solutions of Monotone Stochastic Equations""; ""2.2 Harnack Inequalities for 1""; ""2.3 Harnack Inequalities for (0,1)""; ""2.4 Applications to Specific Models ""; ""2.4.1 Stochastic Generalized Porous Media Equations""; ""2.4.2 Stochastic p-Laplacian Equations"" ""2.4.3 Stochastic Generalized Fast-Diffusion Equations""""Chapter 3 Semilinear Stochastic Partial Differential Equations""; ""3.1 Mild Solutions and Finite-Dimensional Approximations""; ""3.2 Additive Noise""; ""3.2.1 Harnack Inequalities and Bismut Formula""; ""3.2.2 Shift Harnack Inequalities and Integration by PartsFormula""; ""3.3 Multiplicative Noise: The Log-Harnack Inequality""; ""3.3.1 The Main Result""; ""3.3.2 Application to White-Noise-Driven SPDEs""; ""3.4 Multiplicative Noise: Harnack Inequality with Power""; ""3.4.1 Construction of the Coupling"" ""3.4.2 Proof of Theorem 3.4.1""""3.5 Multiplicative Noise: Bismut Formula""; ""Chapter 4 Stochastic Functional (Partial) Differential Equations""; ""4.1 Solutions and Finite-Dimensional Approximations""; ""4.1.1 Stochastic Functional Differential Equations""; ""4.1.2 Semilinear Stochastic Functional Partial Differential Equations""; ""4.2 Elliptic Stochastic Functional Partial Differential Equations with Additive Noise""; ""4.2.1 Harnack Inequalities and Bismut Formula""; ""4.2.2 Shift Harnack Inequalities and Integration by PartsFormulas""; ""4.2.3 Extensions to Semilinear SDPDEs"" ""4.3 Elliptic Stochastic Functional Partial Differential Equations with Multiplicative Noise""""4.3.1 Log-Harnack Inequality""; ""4.3.1.1 Proofs of (i)""; ""4.3.1.2 Proof of (ii)""; ""4.3.1.3 Proof of (iii)""; ""4.3.2 Harnack Inequality with Power""; ""4.3.3 Bismut Formulas for Semilinear SDPDEs""; ""4.4 Stochastic Functional Hamiltonian System""; ""4.4.1 Main Result and Consequences""; ""4.4.2 Proof of Theorem 4.4.1""; ""4.4.3 Proofs of Corollary 4.4.3 and Theorem 4.4.5 ""; ""Glossary""; ""References""; ""Index""
Series Title: SpringerBriefs in mathematics
Responsibility: by Feng-Yu Wang.

Abstract:

In this book the author presents a self-contained account of Harnack inequalities and applications for the semigroup of solutions to stochastic partial and delayed differential equations. Since the semigroup refers to Fokker-Planck equations on infinite-dimensional spaces, the Harnack inequalities the author investigates are dimension-free. This is an essentially different point from the above mentioned classical Harnack inequalities. Moreover, the main tool in the study is a new coupling method (called coupling by change of measures) rather than the usual maximum principle in the current literature.

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