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Contents: Azencott, R. : Large deviations and applications.-
Freidlin, Mark I. Semi-linear PDE's and limit theorems for large
deviations- Varadhan, Srinivasa R.S.: Large deviations and
applications.
This volume contains the text of four sets of lectures delivered at
the third session of the Summer School organized by C.I.M.E.
(Centro Internazionale Matematico Estivo). These texts are preceded
by an introduction written by C. Cercignani and M. Pulvirenti which
summarizes the present status in the area of Nonequilibrium
Problems in Many-Particle Systems and tries to put the contents of
the different sets of lectures in the right perspective, in order
to orient the reader. The lectures deal with the global existence
of weak solutions for kinetic models and related topics, the basic
concepts of non-standard analysis and their application to gas
kinetics, the kinetic equations for semiconductors and the entropy
methods in the study of hydrodynamic limits. CONTENTS: C.
Cercignani, M. Pulvirenti: Nonequilibrium Problems in Many-Particle
Systems. An Introduction.- L. Arkeryd: Some Examples of NSA in
Kinetic Theory.- P.L. Lions: Global Solutions of Kinetic Models and
Related Problems.- P.A. Markowich: Kinetic Models for
Semiconductors.- S.R.S. Varadhan: Entropy Methods in Hydrodynamic
Scaling.
From the Preface: Srinivasa Varadhan began his research career at
the Indian Statistical Institute (ISI), Calcutta, where he started
as a graduate student in 1959. His first paper appeared in Sankhya,
the Indian Journal of Statistics in 1962. Together with his fellow
students V. S. Varadarajan, R. Ranga Rao and K. R. Parthasarathy,
Varadhan began the study of probability on topological groups and
on Hilbert spaces, and quickly gained an international reputation.
At this time Varadhan realised that there are strong connections
between Markov processes and differential equations, and in 1963 he
came to the Courant Institute in New York, where he has stayed ever
since. Here he began working with the probabilists Monroe Donsker
and Marc Kac, and a graduate student named Daniel Stroock. He wrote
a series of papers on the Martingale Problem and Diffusions
together with Stroock, and another series of papers on Large
Deviations together with Donsker. With this work Varadhan's
reputation as one of the leading mathematicians of the time was
firmly established. Since then he has contributed to several other
areas of probability, analysis and physics, and collaborated with
numerous distinguished mathematicians. Varadhan was awarded the
Abel Prize in 2007. These Collected Works contain all his research
papers over the half-century spanning 1962 to early 2012. Volume I
includes the introductory material, the papers on limit theorems
and review articles.
From the Preface: Srinivasa Varadhan began his research career at
the Indian Statistical Institute (ISI), Calcutta, where he started
as a graduate student in 1959. His first paper appeared in Sankhya,
the Indian Journal of Statistics in 1962. Together with his fellow
students V. S. Varadarajan, R. Ranga Rao and K. R. Parthasarathy,
Varadhan began the study of probability on topological groups and
on Hilbert spaces, and quickly gained an international reputation.
At this time Varadhan realised that there are strong connections
between Markov processes and differential equations, and in 1963 he
came to the Courant Institute in New York, where he has stayed ever
since. Here he began working with the probabilists Monroe Donsker
and Marc Kac, and a graduate student named Daniel Stroock. He wrote
a series of papers on the Martingale Problem and Diffusions
together with Stroock, and another series of papers on Large
Deviations together with Donsker. With this work Varadhan's
reputation as one of the leading mathematicians of the time was
firmly established. Since then he has contributed to several other
areas of probability, analysis and physics, and collaborated with
numerous distinguished mathematicians. Varadhan was awarded the
Abel Prize in 2007. These Collected Works contain all his research
papers over the half-century spanning 1962 to early 2012. Volume II
includes the papers on PDE, SDE, diffusions, and random media.
From the Preface: Srinivasa Varadhan began his research career at
the Indian Statistical Institute (ISI), Calcutta, where he started
as a graduate student in 1959. His first paper appeared in Sankhya,
the Indian Journal of Statistics in 1962. Together with his fellow
students V. S. Varadarajan, R. Ranga Rao and K. R. Parthasarathy,
Varadhan began the study of probability on topological groups and
on Hilbert spaces, and quickly gained an international reputation.
At this time Varadhan realised that there are strong connections
between Markov processes and differential equations, and in 1963 he
came to the Courant Institute in New York, where he has stayed ever
since. Here he began working with the probabilists Monroe Donsker
and Marc Kac, and a graduate student named Daniel Stroock. He wrote
a series of papers on the Martingale Problem and Diffusions
together with Stroock, and another series of papers on Large
Deviations together with Donsker. With this work Varadhan's
reputation as one of the leading mathematicians of the time was
firmly established. Since then he has contributed to several other
areas of probability, analysis and physics, and collaborated with
numerous distinguished mathematicians. Varadhan was awarded the
Abel Prize in 2007. These Collected Works contain all his research
papers over the half-century spanning 1962 to early 2012. Volume
III includes the papers on large deviations.
From the Preface: Srinivasa Varadhan began his research career at
the Indian Statistical Institute (ISI), Calcutta, where he started
as a graduate student in 1959. His first paper appeared in Sankhya,
the Indian Journal of Statistics in 1962. Together with his fellow
students V. S. Varadarajan, R. Ranga Rao and K. R. Parthasarathy,
Varadhan began the study of probability on topological groups and
on Hilbert spaces, and quickly gained an international reputation.
At this time Varadhan realised that there are strong connections
between Markov processes and differential equations, and in 1963 he
came to the Courant Institute in New York, where he has stayed ever
since. Here he began working with the probabilists Monroe Donsker
and Marc Kac, and a graduate student named Daniel Stroock. He wrote
a series of papers on the Martingale Problem and Diffusions
together with Stroock, and another series of papers on Large
Deviations together with Donsker. With this work Varadhan's
reputation as one of the leading mathematicians of the time was
firmly established. Since then he has contributed to several other
areas of probability, analysis and physics, and collaborated with
numerous distinguished mathematicians. Varadhan was awarded the
Abel Prize in 2007. These Collected Works contain all his research
papers over the half-century spanning 1962 to early 2012. Volume IV
includes the papers on particle systems.
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Harmonic Analysis (Paperback)
S. R. S. Varadhan, Courant Institute of Mathematical Sciences at New York University
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R1,049
Discovery Miles 10 490
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Ships in 12 - 17 working days
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Harmonic Analysis is an important tool that plays a vital role in
many areas of mathematics as well as applications. It studies
functions by decomposing them into components that are special
functions. A prime example is decomposing a periodic function into
a linear combination of sines and cosines. The subject is vast, and
this book covers only the selection of topics that was dealt with
in the course given at the Courant Institute in 2000 and 2019.
These include standard topics like Fourier series and Fourier
transforms of functions, as well as issues of convergence of Abel,
Feier, and Poisson sums. At a slightly more advanced level the book
studies convolutions with singular integrals, fractional
derivatives, Sobolev spaces, embedding theorems, Hardy spaces, and
BMO. Applications to elliptic partial differential equations and
prediction theory are explored. Some space is devoted to harmonic
analysis on compact non-Abelian groups and their representations,
including some details about two groups: the permutation group and
SO(3). The text contains exercises at the end of most chapters and
is suitable for advanced undergraduate students as well as first-
or second-year graduate students specializing in the areas of
analysis, PDE, probability or applied mathematics.
The central and distinguishing feature shared by all the
contributions made by K. Ito is the extraordinary insight which
they convey. Reading his papers, one should try to picture the
intellectual setting in which he was working. At the time when he
was a student in Tokyo during the late 1930s, probability theory
had only recently entered the age of continuous-time stochastic
processes: N. Wiener had accomplished his amazing construction
little more than a decade earlier (Wiener, N. , "Differential
space," J. Math. Phys. 2, (1923)), Levy had hardly begun the
mysterious web he was to eventually weave out of Wiener's P~!hs,
the generalizations started by Kolmogorov (Kol mogorov, A. N. ,
"Uber die analytische Methoden in der Wahrscheinlichkeitsrechnung,"
Math Ann. 104 (1931)) and continued by Feller (Feller, W. , "Zur
Theorie der stochastischen Prozesse," Math Ann. 113, (1936))
appeared to have little if anything to do with probability theory,
and the technical measure-theoretic tours de force of J. L. Doob
(Doob, J. L. , "Stochastic processes depending on a continuous
parameter, " TAMS 42 (1937)) still appeared impregnable to all but
the most erudite. Thus, even at the established mathematical
centers in Russia, Western Europe, and America, the theory of
stochastic processes was still in its infancy and the student who
was asked to learn the subject had better be one who was ready to
test his mettle.
This book gathers selected papers presented at the International
Conference on Advances in Applied Probability and Stochastic
Processes, held at CMS College, Kerala, India, on 7-10 January
2019. It showcases high-quality research conducted in the field of
applied probability and stochastic processes by focusing on
techniques for the modelling and analysis of systems evolving with
time. Further, it discusses the applications of stochastic
modelling in queuing theory, reliability, inventory, financial
mathematics, operations research, and more. This book is intended
for a broad audience, ranging from researchers interested in
applied probability, stochastic modelling with reference to queuing
theory, inventory, and reliability, to those working in industries
such as communication and computer networks, distributed
information systems, next-generation communication systems,
intelligent transportation networks, and financial markets.
This book gathers selected papers presented at the International
Conference on Advances in Applied Probability and Stochastic
Processes, held at CMS College, Kerala, India, on 7-10 January
2019. It showcases high-quality research conducted in the field of
applied probability and stochastic processes by focusing on
techniques for the modelling and analysis of systems evolving with
time. Further, it discusses the applications of stochastic
modelling in queuing theory, reliability, inventory, financial
mathematics, operations research, and more. This book is intended
for a broad audience, ranging from researchers interested in
applied probability, stochastic modelling with reference to queuing
theory, inventory, and reliability, to those working in industries
such as communication and computer networks, distributed
information systems, next-generation communication systems,
intelligent transportation networks, and financial markets.
The theory of large deviations deals with rates at which
probabilities of certain events decay as a natural parameter in the
problem varies. This book, which is based on a graduate course on
large deviations at the Courant Institute, focuses on three
concrete sets of examples: (i) diffusions with small noise and the
exit problem, (ii) large time behavior of Markov processes and
their connection to the Feynman-Kac formula and the related large
deviation behavior of the number of distinct sites visited by a
random walk, and (iii) interacting particle systems, their scaling
limits, and large deviations from their expected limits. For the
most part the examples are worked out in detail, and in the process
the subject of large deviations is developed. The book will give
the reader a flavor of how large deviation theory can help in
problems that are not posed directly in terms of large deviations.
The reader is assumed to have some familiarity with probability,
Markov processes, and interacting particle systems.
This is a brief introduction to stochastic processes studying
certain elementary continuous-time processes. After a description
of the Poisson process and related processes with independent
increments as well as a brief look at Markov processes with a
finite number of jumps, the author proceeds to introduce Brownian
motion and to develop stochastic integrals and Ito's theory in the
context of one-dimensional diffusion processes. The book ends with
a brief survey of the general theory of Markov processes. The book
is based on courses given by the author at the Courant Institute
and can be used as a sequel to the author's successful book
Probability Theory in this series. Information for our
distributors: Titles in this series are co-published with the
Courant Institute of Mathematical Sciences at New York University.
Many situations exist in which solutions to problems are
represented as function space integrals. Such representations can
be used to study the qualitative properties of the solutions and to
evaluate them numerically using Monte Carlo methods. The emphasis
in this book is on the behavior of solutions in special situations
when certain parameters get large or small.
This volume presents topics in probability theory covered during a
first-year graduate course given at the Courant Institute of
Mathematical Sciences, USA. The necessary background material in
measure theory is developed, including the standard topics, such as
extension theorem, construction of measures, integration, product
spaces, Radon-Nikodym theorem, and conditional expectation In the
first part of the book, characteristic functions are introduced,
followed by the study of weak convergence of probability
distributions. Then both the weak and strong limit theorems for
sums of independent random variables are proved, including the weak
and strong laws of large numbers, central limit theorems, laws of
the iterated logarithm, and the Kolmogorov three series theorem.
The first part concludes with infinitely divisible distributions
and limit theorems for sums of uniformly infinitesimal independent
random variables. The second part of the book mainly deals with
dependent random variables, particularly martingales and Markov
chains. Topics include standard results regarding discrete
parameter martingales and Doob's inequalities.
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