Analysis of Stochastic Partial Differential Equations

· CBMS Regional Conference Series in Mathematics Cartea 119 · American Mathematical Soc.
Carte electronică
116
Pagini
Evaluările și recenziile nu sunt verificate Află mai multe

Despre această carte electronică

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.

Despre autor

Nothing provided

Evaluează cartea electronică

Spune-ne ce crezi.

Informații despre lectură

Smartphone-uri și tablete
Instalează aplicația Cărți Google Play pentru Android și iPad/iPhone. Se sincronizează automat cu contul tău și poți să citești online sau offline de oriunde te afli.
Laptopuri și computere
Poți să asculți cărțile audio achiziționate pe Google Play folosind browserul web al computerului.
Dispozitive eReader și alte dispozitive
Ca să citești pe dispozitive pentru citit cărți electronice, cum ar fi eReaderul Kobo, trebuie să descarci un fișier și să îl transferi pe dispozitiv. Urmează instrucțiunile detaliate din Centrul de ajutor pentru a transfera fișiere pe dispozitivele eReader compatibile.