Analysis of stochastic partial differential equations

著者

• Khoshnevisan, Davar

書誌事項

Analysis of stochastic partial differential equations

Davar Khoshnevisan

（Regional conference series in mathematics, no. 119）

Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, c2014

注記

"With support from the National Science Foundation"

"NSF-CBMS Regional Conference in the Mathematical Sciences: Analysis of Stochastic Partial Differential Equations held at Michigan State University, East Lansing, Michigan, August 19-23, 2013"--T.p. verso

Bibliography: p. 111-116

内容説明・目次

内容説明

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.

目次

Contents Prelude Wiener integrals A linear heat equation Walsh-Dalang integrals A non-linear heat equation Intermezzo: A parabolic Anderson model Intermittency Intermittency fronts Intermittency islands Correlation length Some special integrals A Burkholder-Davis-Gundy inequality Regularity theory Bibliography

「Nielsen BookData」 より

詳細情報

• NII書誌ID(NCID): BB15907424
• ISBN:
  • 9781470415471
• LCCN: 2014003696
• 出版国コード: us
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Providence, R.I.
• ページ数/冊数: viii, 116 p.
• 大きさ: 26 cm
• 分類:
  • LCC : QA274.25
  • DC23 : 519.2/2
• 件名:
  • LCSH : Stochastic partial differential equations -- Congresses
• 親書誌ID:
  • BA0000944X