Softcover ISBN:  9781470415471 
Product Code:  CBMS/119 
List Price:  $40.00 
Individual Price:  $32.00 
Electronic ISBN:  9781470417123 
Product Code:  CBMS/119.E 
List Price:  $37.00 
Individual Price:  $29.60 

Book DetailsCBMS Regional Conference Series in MathematicsVolume: 119; 2014; 116 ppMSC: Primary 60; Secondary 35;
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 twoparameter 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 indepth look at intermittency properties of the solution to semilinear stochastic heat equations. Specific topics include stochastic integrals à la Norbert Wiener, an infinitedimensional Itôtype 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.A copublication of the AMS and CBMS.
ReadershipGraduate students and research mathematicians interested in stochastic PDEs.

Table of Contents

Chapters

1. Prelude

2. Wiener integrals

3. A linear heat equation

4. WalshDalang integrals

5. A nonlinear 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 BurkholderDavisGundy inequality

Appendix C. Regularity theory


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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 twoparameter 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 indepth look at intermittency properties of the solution to semilinear stochastic heat equations. Specific topics include stochastic integrals à la Norbert Wiener, an infinitedimensional Itôtype 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.
A copublication of the AMS and CBMS.
Graduate students and research mathematicians interested in stochastic PDEs.

Chapters

1. Prelude

2. Wiener integrals

3. A linear heat equation

4. WalshDalang integrals

5. A nonlinear 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 BurkholderDavisGundy inequality

Appendix C. Regularity theory