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Analysis of Stochastic Partial Differential Equations
 
Davar Khoshnevisan University of Utah, Salt Lake City, UT
A co-publication of the AMS and CBMS
Analysis of Stochastic Partial Differential Equations
Softcover ISBN:  978-1-4704-1547-1
Product Code:  CBMS/119
List Price: $42.00
Individual Price: $33.60
eBook ISBN:  978-1-4704-1712-3
Product Code:  CBMS/119.E
List Price: $39.00
Individual Price: $31.20
Softcover ISBN:  978-1-4704-1547-1
eBook: ISBN:  978-1-4704-1712-3
Product Code:  CBMS/119.B
List Price: $81.00 $61.50
Analysis of Stochastic Partial Differential Equations
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Analysis of Stochastic Partial Differential Equations
Davar Khoshnevisan University of Utah, Salt Lake City, UT
A co-publication of the AMS and CBMS
Softcover ISBN:  978-1-4704-1547-1
Product Code:  CBMS/119
List Price: $42.00
Individual Price: $33.60
eBook ISBN:  978-1-4704-1712-3
Product Code:  CBMS/119.E
List Price: $39.00
Individual Price: $31.20
Softcover ISBN:  978-1-4704-1547-1
eBook ISBN:  978-1-4704-1712-3
Product Code:  CBMS/119.B
List Price: $81.00 $61.50
  • Book Details
     
     
    CBMS Regional Conference Series in Mathematics
    Volume: 1192014; 116 pp
    MSC: 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 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 à la Norbert Wiener, an infinite-dimensional Itô-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.

    A co-publication of the AMS and CBMS.

    Readership

    Graduate students and research mathematicians interested in stochastic PDEs.

  • Table of Contents
     
     
    • Chapters
    • 1. Prelude
    • 2. Wiener integrals
    • 3. A linear heat equation
    • 4. Walsh-Dalang 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. Regularity theory
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 1192014; 116 pp
MSC: 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 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 à la Norbert Wiener, an infinite-dimensional Itô-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.

A co-publication of the AMS and CBMS.

Readership

Graduate students and research mathematicians interested in stochastic PDEs.

  • Chapters
  • 1. Prelude
  • 2. Wiener integrals
  • 3. A linear heat equation
  • 4. Walsh-Dalang 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. Regularity theory
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
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