Analysis of stochastic partial differential equations

By: Davar KhoshnevisanMaterial type: TextTextSeries: CBMS Regional Conference Series in Mathematics ; No. 119Publication details: Rhode Island: American Mathematical Society, [c2017]Description: 116 pISBN: 978-1-4704-1547-1Subject(s): MathematicsLOC classification: QA274.25
Contents:
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
Summary: 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. --- summary provided by publisher
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Item type Current library Collection Shelving location Call number Status Notes Date due Barcode Item holds
Book Book ICTS
Mathematic Rack No 5 QA274.25 (Browse shelf (Opens below)) Available Billno:IN 003 582; Billdate: 2018-01-11 00883
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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

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. --- summary provided by publisher

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