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The present book is based on a course developed as partofthe large
NSF-funded
GatewayCoalitionInitiativeinEngineeringEducationwhichincludedCaseWest
ern Reserve University, Columbia University, Cooper Union, Drexel
University, Florida International University, New Jersey Institute
ofTechnology, Ohio State University, University ofPennsylvania,
Polytechnic University, and Universityof South Carolina. The
Coalition aimed to restructure the engineering curriculum by
incorporating the latest technological innovations and tried to
attract more and betterstudents to engineering and science.
Draftsofthis textbookhave been used since
1992instatisticscoursestaughtatCWRU, IndianaUniversity,
Bloomington, and at the universities in Gottingen, Germany, and
Grenoble, France. Another purpose of this project was to develop a
courseware that would take advantage ofthe Electronic Learning
Environment created by CWRUnet-the all fiber-optic Case Western
Reserve University computer network, and its ability to let
students run Mathematica experiments and projects in their
dormitory rooms, and interactpaperlessly with the instructor.
Theoretically, onecould try togothroughthisbook withoutdoing
Mathematica experimentsonthecomputer,
butitwouldbelikeplayingChopin's Piano Concerto in E-minor, or Pink
Floyd's The Wall, on an accordion. One would get an idea ofwhatthe
tune was without everexperiencing the full richness andpowerofthe
entire composition, and the whole ambience would be miscued."
This IMA Volume in Mathematics and its Applications NONLINEAR
STOCHASTIC PDEs: HYDRODYNAMIC LIMIT AND BURGERS' TURBULENCE is
based on the proceedings of the period of concentration on Stochas
tic Methods for Nonlinear PDEs which was an integral part of the
1993- 94 IMA program on "Emerging Applications of Probability." We
thank Tadahisa Funaki and Wojbor A. Woyczynski for organizing this
meeting and for editing the proceedings. We also take this
opportunity to thank the National Science Foundation and the Army
Research Office, whose financial support made this workshop
possible. A vner Friedman Willard Miller, Jr. xiii PREFACE A
workshop on Nonlinear Stochastic Partial Differential Equations was
held during the week of March 21 at the Institute for Mathematics
and Its Applications at the University of Minnesota. It was part of
the Special Year on Emerging Applications of Probability program
put together by an organizing committee chaired by J. Michael
Steele. The selection of topics reflected personal interests of the
organizers with two areas of emphasis: the hydrodynamic limit
problems and Burgers' turbulence and related models. The talks and
the papers appearing in this volume reflect a number of research
directions that are currently pursued in these areas."
This book studies the foundations of the theory of linear and
nonlinear forms in single and multiple random variables including
the single and multiple random series and stochastic integrals,
both Gaussian and non-Gaussian. This subject is intimately
connected with a number of classical problems of probability theory
such as the summation of independent random variables, martingale
theory, and Wiener's theory of polynomial chaos. The book contains
a number of older results as well as more recent, or previously
unpublished, results. The emphasis is on domination principles for
comparison of different sequences of random variables and on
decoupling techniques. These tools prove very useful in many areas
ofprobability and analysis, and the book contains only their
selected applications. On the other hand, the use of the Fourier
transform - another classical, but limiting, tool in probability
theory - has been practically eliminated. The book is addressed to
researchers and graduate students in prob ability theory,
stochastic processes and theoretical statistics, as well as in
several areas oftheoretical physics and engineering. Although the
ex position is conducted - as much as is possible - for random
variables with values in general Banach spaces, we strive to avoid
methods that would depend on the intricate geometric properties of
normed spaces. As a result, it is possible to read the book in its
entirety assuming that all the Banach spaces are simply finite
dimensional Euclidean spaces."
The present book is based on a course developed as partofthe large
NSF-funded
GatewayCoalitionInitiativeinEngineeringEducationwhichincludedCaseWest
ern Reserve University, Columbia University, Cooper Union, Drexel
University, Florida International University, New Jersey Institute
ofTechnology, Ohio State University, University ofPennsylvania,
Polytechnic University, and Universityof South Carolina. The
Coalition aimed to restructure the engineering curriculum by
incorporating the latest technological innovations and tried to
attract more and betterstudents to engineering and science.
Draftsofthis textbookhave been used since
1992instatisticscoursestaughtatCWRU, IndianaUniversity,
Bloomington, and at the universities in Gottingen, Germany, and
Grenoble, France. Another purpose of this project was to develop a
courseware that would take advantage ofthe Electronic Learning
Environment created by CWRUnet-the all fiber-optic Case Western
Reserve University computer network, and its ability to let
students run Mathematica experiments and projects in their
dormitory rooms, and interactpaperlessly with the instructor.
Theoretically, onecould try togothroughthisbook withoutdoing
Mathematica experimentsonthecomputer,
butitwouldbelikeplayingChopin's Piano Concerto in E-minor, or Pink
Floyd's The Wall, on an accordion. One would get an idea ofwhatthe
tune was without everexperiencing the full richness andpowerofthe
entire composition, and the whole ambience would be miscued."
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