Holder Sobolev Regularity Of The Solution To The Stochastic Wave Equation In Dimension Three

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Holder Sobolev Regularity Of The Solution To The Stochastic Wave Equation In Dimension Three

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Author : Robert C. Dalang
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-04-10

Holder Sobolev Regularity Of The Solution To The Stochastic Wave Equation In Dimension Three written by Robert C. Dalang and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-10 with Mathematics categories.

The authors study the sample path regularity of the solution of a stochastic wave equation in spatial dimension $d=3$. The driving noise is white in time and with a spatially homogeneous covariance defined as a product of a Riesz kernel and a smooth function. The authors prove that at any fixed time, a.s., the sample paths in the spatial variable belong to certain fractional Sobolev spaces. In addition, for any fixed $x\in\mathbb{R}^3$, the sample paths in time are Holder continuous functions. Further, the authors obtain joint Holder continuity in the time and space variables. Their results rely on a detailed analysis of properties of the stochastic integral used in the rigourous formulation of the s.p.d.e., as introduced by Dalang and Mueller (2003). Sharp results on one- and two-dimensional space and time increments of generalized Riesz potentials are a crucial ingredient in the analysis of the problem. For spatial covariances given by Riesz kernels, the authors show that the Holder exponents that they obtain are optimal.

General Stochastic Measures

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Author : Vadym M. Radchenko
language : en
Publisher: John Wiley & Sons
Release Date : 2022-09-21

General Stochastic Measures written by Vadym M. Radchenko and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-21 with Mathematics categories.

This book is devoted to the study of stochastic measures (SMs). An SM is a sigma-additive in probability random function, defined on a sigma-algebra of sets. SMs can be generated by the increments of random processes from many important classes such as square-integrable martingales and fractional Brownian motion, as well as alpha-stable processes. SMs include many well-known stochastic integrators as partial cases. General Stochastic Measures provides a comprehensive theoretical overview of SMs, including the basic properties of the integrals of real functions with respect to SMs. A number of results concerning the Besov regularity of SMs are presented, along with equations driven by SMs, types of solution approximation and the averaging principle. Integrals in the Hilbert space and symmetric integrals of random functions are also addressed. The results from this book are applicable to a wide range of stochastic processes, making it a useful reference text for researchers and postgraduate or postdoctoral students who specialize in stochastic analysis.

H Lder Sobolev Regularity Of The Solution To The Stochastic Wave Equation In Dimension 3

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Author : Robert C. Dalang
language : en
Publisher:
Release Date : 2005

H Lder Sobolev Regularity Of The Solution To The Stochastic Wave Equation In Dimension 3 written by Robert C. Dalang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with categories.

A Minicourse On Stochastic Partial Differential Equations

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Author : Robert C. Dalang
language : en
Publisher: Springer Science & Business Media
Release Date : 2009

A Minicourse On Stochastic Partial Differential Equations written by Robert C. Dalang and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.

This title contains lectures that offer an introduction to modern topics in stochastic partial differential equations and bring together experts whose research is centered on the interface between Gaussian analysis, stochastic analysis, and stochastic PDEs.

Mathematical Reviews

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Author :
language : en
Publisher:
Release Date : 2001

Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.

Dissertation Abstracts International

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Author :
language : en
Publisher:
Release Date : 1998

Dissertation Abstracts International written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Dissertations, Academic categories.

Differentiable Measures And The Malliavin Calculus

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Author : Vladimir Igorevich Bogachev
language : en
Publisher: American Mathematical Soc.
Release Date : 2010-07-21

Differentiable Measures And The Malliavin Calculus written by Vladimir Igorevich Bogachev and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-21 with Mathematics categories.

This book provides the reader with the principal concepts and results related to differential properties of measures on infinite dimensional spaces. In the finite dimensional case such properties are described in terms of densities of measures with respect to Lebesgue measure. In the infinite dimensional case new phenomena arise. For the first time a detailed account is given of the theory of differentiable measures, initiated by S. V. Fomin in the 1960s; since then the method has found many various important applications. Differentiable properties are described for diverse concrete classes of measures arising in applications, for example, Gaussian, convex, stable, Gibbsian, and for distributions of random processes. Sobolev classes for measures on finite and infinite dimensional spaces are discussed in detail. Finally, we present the main ideas and results of the Malliavin calculus--a powerful method to study smoothness properties of the distributions of nonlinear functionals on infinite dimensional spaces with measures. The target readership includes mathematicians and physicists whose research is related to measures on infinite dimensional spaces, distributions of random processes, and differential equations in infinite dimensional spaces. The book includes an extensive bibliography on the subject.

Functional Analysis Sobolev Spaces And Partial Differential Equations

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Author : Haim Brezis
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-10

Functional Analysis Sobolev Spaces And Partial Differential Equations written by Haim Brezis and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-10 with Mathematics categories.

This textbook is a completely revised, updated, and expanded English edition of the important Analyse fonctionnelle (1983). In addition, it contains a wealth of problems and exercises (with solutions) to guide the reader. Uniquely, this book presents in a coherent, concise and unified way the main results from functional analysis together with the main results from the theory of partial differential equations (PDEs). Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics. Since the French book was first published, it has been translated into Spanish, Italian, Japanese, Korean, Romanian, Greek and Chinese. The English edition makes a welcome addition to this list.

Partial Differential Equations In Action

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Author : Sandro Salsa
language : en
Publisher: Springer
Release Date : 2015-04-24

Partial Differential Equations In Action written by Sandro Salsa and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-24 with Mathematics categories.

The book is intended as an advanced undergraduate or first-year graduate course for students from various disciplines, including applied mathematics, physics and engineering. It has evolved from courses offered on partial differential equations (PDEs) over the last several years at the Politecnico di Milano. These courses had a twofold purpose: on the one hand, to teach students to appreciate the interplay between theory and modeling in problems arising in the applied sciences, and on the other to provide them with a solid theoretical background in numerical methods, such as finite elements. Accordingly, this textbook is divided into two parts. The first part, chapters 2 to 5, is more elementary in nature and focuses on developing and studying basic problems from the macro-areas of diffusion, propagation and transport, waves and vibrations. In turn the second part, chapters 6 to 11, concentrates on the development of Hilbert spaces methods for the variational formulation and the analysis of (mainly) linear boundary and initial-boundary value problems.

Elliptic Partial Differential Equations

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Author : Lucio Boccardo
language : en
Publisher: ISSN
Release Date : 2014

Elliptic Partial Differential Equations written by Lucio Boccardo and has been published by ISSN this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Differential equations, Elliptic categories.

The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 30 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob.