Online Public Access Catalogue (OPAC)
Library,Documentation and Information Science Division

“A research journal serves that narrow

borderland which separates the known from the unknown”

-P.C.Mahalanobis


Image from Google Jackets

Analysis of stochastic partial differential equations / Davar Khoshnevisan.

By: Contributor(s): Material type: TextTextSeries: CBMS regional conference series in mathematics ; no 119.Publication details: Providence : American Mathematical Society 2014.Description: viii, 116 p. : illustrations ; 26 cmISBN:
  • 9781470415471 (softcover : alk. paper)
Subject(s): DDC classification:
  • 510 23 C748
Contents:
1. Prelude -- 2. Wiener integrals -- 3. A linear heat equation -- 4. Walsh-Damang integrals -- 5. A non-linear heat equation -- 6. Intermezzo: A parabolic Anderson model -- 7. Intermittency -- 8. Intermittency fronts -- 9. Intermittency islands -- 10. Correlation length -- Appendix A: Some special integrals -- Appendix B: A Burkholder-Davis-Gundy inequality -- Appendix C: Reguarity theory-- Bibliography.
Summary: The general area of stochastic PDEs is interesting to mathematicians because it contains an enormous number of challenging open problems. There is also a great deal of interest in this topic because it has deep applications in disciplines that range from applied mathematics, statistical mechanics, and theoretical physics, to theoretical neuroscience, theory of complex chemical reactions [including polymer science], fluid dynamics, and mathematical finance. The stochastic PDEs that are studied in this book are similar to the familiar PDE for heat in a thin rod, but with the additional restriction that the external forcing density is a two-parameter stochastic process, or what is more commonly the case, the forcing is a "random noise," also known as a "generalized random field." At several points in the lectures, there are examples that highlight the phenomenon that stochastic PDEs are not a subset of PDEs. In fact, the introduction of noise in some partial differential equations can bring about not a small perturbation, but truly fundamental changes to the system that the underlying PDE is attempting to describe. The topics covered include a brief introduction to the stochastic heat equation, structure theory for the linear stochastic heat equation, and an in-depth look at intermittency properties of the solution to semilinear stochastic heat equations. Specific topics include stochastic integrals a la Norbert Wiener, an infinite-dimensional Ito-type stochastic integral, an example of a parabolic Anderson model, and intermittency fronts. There are many possible approaches to stochastic PDEs. The selection of topics and techniques presented here are informed by the guiding example of the stochastic heat equation.
Tags from this library: No tags from this library for this title. Log in to add tags.

"Supported by the National Science Foundation."

Includes bibliographical references (pages 111-116).

1. Prelude --
2. Wiener integrals --
3. A linear heat equation --
4. Walsh-Damang integrals --
5. A non-linear heat equation --
6. Intermezzo: A parabolic Anderson model --
7. Intermittency --
8. Intermittency fronts --
9. Intermittency islands --
10. Correlation length --
Appendix A: Some special integrals --
Appendix B: A Burkholder-Davis-Gundy inequality --
Appendix C: Reguarity theory--
Bibliography.

The general area of stochastic PDEs is interesting to mathematicians because it contains an enormous number of challenging open problems. There is also a great deal of interest in this topic because it has deep applications in disciplines that range from applied mathematics, statistical mechanics, and theoretical physics, to theoretical neuroscience, theory of complex chemical reactions [including polymer science], fluid dynamics, and mathematical finance. The stochastic PDEs that are studied in this book are similar to the familiar PDE for heat in a thin rod, but with the additional restriction that the external forcing density is a two-parameter stochastic process, or what is more commonly the case, the forcing is a "random noise," also known as a "generalized random field." At several points in the lectures, there are examples that highlight the phenomenon that stochastic PDEs are not a subset of PDEs. In fact, the introduction of noise in some partial differential equations can bring about not a small perturbation, but truly fundamental changes to the system that the underlying PDE is attempting to describe. The topics covered include a brief introduction to the stochastic heat equation, structure theory for the linear stochastic heat equation, and an in-depth look at intermittency properties of the solution to semilinear stochastic heat equations. Specific topics include stochastic integrals a la Norbert Wiener, an infinite-dimensional Ito-type stochastic integral, an example of a parabolic Anderson model, and intermittency fronts. There are many possible approaches to stochastic PDEs. The selection of topics and techniques presented here are informed by the guiding example of the stochastic heat equation.

There are no comments on this title.

to post a comment.
Library, Documentation and Information Science Division, Indian Statistical Institute, 203 B T Road, Kolkata 700108, INDIA
Phone no. 91-33-2575 2100, Fax no. 91-33-2578 1412, ksatpathy@isical.ac.in