Series: Lecture Notes in Mathematics, Vol.
1837
2004, VII,315p., Softcover
ISBN: 3-540-20832-1
About this book
This volume contains lectures given at the
31st Probability
Summer School in Saint-Flour (July 8-25,
2001). Simon Tavare?s
lectures serve as an introduction to the
coalescent, and to
inference for ancestral processes in population
genetics. The
stochastic computation methods described
include rejection
methods, importance sampling, Markov chain
Monte Carlo, and
approximate Bayesian methods. Ofer Zeitouni?s
course on "Random
Walks in Random Environment" presents
systematically the
tools that have been introduced to study
the model. A fairly
complete description of available results
in dimension 1 is given.
For higher dimension, the basic techniques
and a discussion of
some of the available results are provided.
The contribution also
includes an updated annotated bibliography
and suggestions for
further reading. Olivier Catoni's course
appears separately as
Vol. 179 of the Lecture Notes in Statistics.
Written for:
Researchers and advanced students
Table of contents
Series: Lecture Notes in Mathematics, Vol.
1838
2004, XI, 254 p., Softcover
ISBN: 3-540-20912-3
About this book
Big Queues aims to give a simple and elegant
account of how large
deviations theory can be applied to queueing
problems. Large
deviations theory is a collection of powerful
results and general
techniques for studying rare events, and
has been applied to
queueing problems in a variety of ways. The
strengths of large
deviations theory are these: it is powerful
enough that one can
answer many questions which are hard to answer
otherwise, and it
is general enough that one can draw broad
conclusions without
relying on special case calculations.
Written for:
Researchers and graduate students in probability
and
mathematically inclined students in engineering
Keywords:
Queues
applied probability
large deviations
Table of contents
Series: Lecture Notes in Mathematics, Vol.
1839
2004, VIII, 170 p., Softcover
ISBN: 3-540-20926-3
About this book
Quantum probability and the theory of operator
algebras are both
concerned with the study of noncommutative
dynamics. Focusing on
stationary processes with discrete-time parameter,
this book
presents (without many prerequisites) some
basic problems of
interest to both fields, on topics including
extensions and
dilations of completely positive maps, Markov
property and
adaptedness, endomorphisms of operator algebras
and the
applications arising from the interplay of
these themes. Much of
the material is new, but many interesting
questions are
accessible even to the reader equipped only
with basic knowledge
of quantum probability and operator algebras.
Written for:
Researchers and graduate students
Keywords:
46L53, 46L55, 47B65, 60G10, 60J05
adapted endomorphism
completely positive
dilation
extension
Table of contents
http://www.springeronline.com/sgw/cda/pageitems/document/cda_downloaddocument/0,10900,0-0-45-107821-0,00.pdf
Series: Probability and its Applications
2004, Approx. 585 p., Hardcover
ISBN: 0-387-20268-4
About this book
This book contains a systematic and self-contained
treatment of
Feynman-Kac path measures, their genealogical
and interacting
particle interpretations, and their applications
to a variety of
problems arising in statistical physics,
biology, and advanced
engineering sciences. Topics include spectral
analysis of Feynman-Kac-Schrodinger
operators, Dirichlet problems with boundary
conditions, finance,
molecular analysis, rare events and directed
polymers simulation,
genetic algorithms, Metropolis-Hastings type
models, as well as
filtering problems and hidden Markov chains.
This text takes
readers in a clear and progressive format
from simple to recent
and advanced topics in pure and applied probability
such as
contraction and annealed properties of non-linear
semi-groups,
functional entropy inequalities, empirical
process convergence,
increasing propagations of chaos, central
limit, and Berry Esseen
type theorems as well as large deviations
principles for strong
topologies on path-distribution spaces. Topics
also include a
body of powerful branching and interacting
particle methods and
worked out illustrations of the key aspect
of the theory. With
practical and easy to use references as well
as deeper and modern
mathematics studies, the book will be of
use to engineers and
researchers in pure and applied mathematics,
statistics, physics,
biology, and operation research who have
a background in
probability and Markov chain theory. Pierre
Del Moral is a
research fellow in mathematics at the C.N.R.S.
(Centre National
de la Recherche Scientifique) at the Laboratoire
de Statistique
et Probabilites of Paul Sabatier University
in Toulouse. He
received his Ph.D. in signal processing at
the LAAS-CNRS (Laboratoire
d'Analyse et Architecture des Systemes) of
Toulouse. He is one of
the principal designers of the modern and
recently developing
theory on particle methods in filtering theory.
He served as a
research engineer in the company Steria-Digilog
from 1992 to 1995
and he has been a visiting professor at Purdue
University and
Princeton University. He is a former associate
editor of the
journal "Stochastic Analysis and Applications".
Table of contents
Introduction.- Feynman-Kac Formulae.- Genealogical
and
Interacting Particle Models.- Stability of
Feynman-Kac Semi-groups.-
Invariant Measures and Related Topics.- Annealing
Properties.-
Asymptotic Behavior.- Propagations of Chaos.-
Central Limit
Theorems.- Large Deviations Principles.-
Feynman-Kac and
Interacting Particle Recipes.- Applications.
Series: Springer Monographs in Mathematics
2004, Approx. 400 p., Hardcover
ISBN: 0-387-20711-2
About this book
This book covers the following three topics
in a manner
accessible to graduate students who have
an understanding of
algebraic number theory and scheme theoretic
algebraic geometry:
1. An elementary construction of Shimura
varieties as moduli of
abelian schemes 2. p-adic deformation theory
of automorphic forms
on Shimura varieties 3. A simple proof of
irreducibility of the
generalized Igusa tower over the Shimura
variety The book starts
with a detailed study of elliptic and Hilbert
modular forms and
reaches to the forefront of research of Shimura
varieties
associated with general classical groups.
The method of
constructing p-adic analytic families and
the proof of
irreducibility was recently discovered by
the author. The area
covered in this book is now a focal point
of research worldwide
with many far-reaching applications that
have led to solutions of
longstanding problems and conjectures. Specifically,
the use of p-adic
elliptic and Hilbert modular forms have proven
essential in
recent breakthroughs in number theory (for
example, the proof of
Fermat's Last Theorem and the Shimura-Taniyama
conjecture by A.
Wiles and others). Haruzo Hida is Professor
of Mathematics at
University of California, Los Angeles. His
previous books include
Modular Forms and Galois Cohomology (Cambridge
University Press
2000) and Geometric Modular Forms and Elliptic
Curves (World
Scientific Publishing Company 2000).
Table of contents
Introduction.- Geometric Reciprocity Laws.-
Modular Curves.-
Hilbert Modular Varieties.- Generalized Eichler-Shimura
Map.-
Moduli Schemes.- Shimura Varieties.- p-Adic
Automorphic Forms.-
Bibliography.