Analysis of Stochastic Partial Differential Equations
Language: English
Published by American Mathematical Society, 2014
- Softcover
- New
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Series: CBMS Regional Conference Series in Mathematics. Num Pages: 116 pages, illustrations (black and white). BIC Classification: PBKJ; PBWL. Category: (P) Professional & Vocational. Dimension: 262 x 183 x 9. Weight in Grams: 238. . 2014. Paperback. . . . . Books ship from the US and Ireland.
Seller Inventory # V9781470415471
- Title
- Analysis of Stochastic Partial Differential Equations
- Author
- Khoshnevisan, Davar
- Publisher
- American Mathematical Society
- Publication year
- 2014
- Condition
- New
- Binding
- Soft cover
- Language
- English
- ISBN 10
- 147041547X
- ISBN 13
- 9781470415471
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.
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Kennys Bookstore
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