1st ed. 2017, XVI, 204 p.
Hardcover
ISBN 978-3-662-54322-1
Series: Probability Theory and Stochastic Modelling, Vol. 80
* Each chapter ends with a set of exercises
* Provides a detailed exposition of optimal asymptotics results for
strongly mixing sequences
* English translation is an updated and revised edition
Presenting tools to aid understanding of asymptotic theory and weakly dependent
processes, this book is devoted to inequalities and limit theorems for sequences of
random variables that are strongly mixing in the sense of Rosenblatt, or absolutely
regular.
The first chapter introduces covariance inequalities under strong mixing or absolute
regularity. These covariance inequalities are applied in Chapters 2, 3 and 4 to moment
inequalities, rates of convergence in the strong law, and central limit theorems. Chapter 5
concerns coupling. In Chapter 6 new deviation inequalities and new moment inequalities
for partial sums via the coupling lemmas of Chapter 5 are derived and applied to the
bounded law of the iterated logarithm. Chapters 7 and 8 deal with the theory of empirical
processes under weak dependence. Lastly, Chapter 9 describes links between ergodicity,
return times and rates of mixing in the case of irreducible Markov chains. Each chapter
ends with a set of exercises.
The book is an updated and extended translation of the French edition entitled "Theorie
asymptotique des processus aleatoires faiblement dependants" (Springer, 2000). It will be
useful for students and researchers in mathematical statistics, econometrics, probability
theory and dynamical systems who are interested in weakly dependent processes.
1st ed. 2017, XVIII, 690 p.
Hardcover
ISBN 978-3-319-53066-6
Series: Probability Theory and Stochastic Modelling, Vol. 82
* Provides a systematic survey of the main available results, with
proofs and references
* Gives a complete presentation of the theory of regular and viscosity
solutions of second-order HJB equations in infinite-dimensional Hilbert spaces
* Reviews alternative approaches to the theory
Providing an introduction to stochastic optimal control in infinite dimension, this book
gives a complete account of the theory of second-order HJB equations in infinitedimensional
Hilbert spaces, focusing on its applicability to associated stochastic optimal
control problems. It features a general introduction to optimal stochastic control,
including basic results (e.g. the dynamic programming principle) with proofs, and
provides examples of applications. A complete and up-to-date exposition of the existing
theory of viscosity solutions and regular solutions of second-order HJB equations in
Hilbert spaces is given, together with an extensive survey of other methods, with a full
bibliography. In particular, Chapter 6, written by M. Fuhrman and G. Tessitore, surveys
the theory of regular solutions of HJB equations arising in infinite-dimensional stochastic
control, via BSDEs. The book is of interest to both pure and applied researchers working
in the control theory of stochastic PDEs, and in PDEs in infinite dimension. Readers from
other fields who want to learn the basic theory will also find it useful. The prerequisites
are: standard functional analysis, the theory of semigroups of operators and its use in the
study of PDEs, some knowledge of the dynamic programming approach to stochastic
optimal control problems in finite dimension, and the basics of stochastic analysis and
stochastic equations in infinite-dimensional spaces.
1st ed. 2017, VIII, 216 p. 2 illus.
Hardcover
ISBN 978-1-4939-7004-9
Series: The IMA Volumes in Mathematics and its Applications, Vol. 161
* Written by leading experts in the field, providing state of the art results
* Chapters derived from workshop talks, annual program seminars,
and research interests of mathematicians at the IMA
* Contains many surveys of active research areas, including open problems
This volume presents some of the research topics discussed at the 2014-2015 Annual
Thematic Program Discrete Structures: Analysis and Applications at the Institute of
Mathematics and its Applications during the Spring 2015 where geometric analysis,
convex geometry and concentration phenomena were the focus.
Leading experts have written surveys of research problems, making state of the art results
more conveniently and widely available. The volume is organized into two parts. Part I
contains those contributions that focus primarily on problems motivated by probability
theory, while Part II contains those contributions that focus primarily on problems
motivated by convex geometry and geometric analysis.
This book will be of use to those who research convex geometry, geometric analysis and
probability directly or apply such methods in other fields.
1st ed. 2017, Approx. 500 p. 85 illus., 70 illus. in color.
Hardcover
ISBN 978-3-319-55235-4
Series: Springer Proceedings in Mathematics & Statistics, Vol. 195
The concepts and techniques presented in this volume originated from the fields of
dynamics, statistics, control theory, computer science and informatics, and are applied
to novel and innovative real-world applications. Over the past few decades, the use
of dynamic systems, control theory, computing, data mining, machine learning and
simulation has gained the attention of numerous researchers from all over the world.
Admirable scientific projects using both model-free and model-based methods coevolved
at today’s research centers and are introduced in conferences around the world, yielding
new scientific advances and helping to solve important real-world problems. One
important area of progress is the bioeconomy, where advances in the life sciences are
used to produce new products in a sustainable and clean manner. In this book, scientists
from all over the world share their latest insights and important findings in the field.
The majority of the contributed papers for this volume were written by participants of
the 3rd International Conference on Dynamics, Games and Science, DGSIII, held at the
University of Porto in February 2014, and at the Berkeley Bioeconomy Conference at the
University of California at Berkeley in March 2014.
The aim of the project of this book “Modeling, Dynamics, Optimization and Bioeconomics
II” follows the same aim as its companion piece, “Modeling, Dynamics, Optimization and
Bioeconomics I,” namely, the exploration of emerging and cutting-edge theories and
methods for modeling, optimization, dynamics and bioeconomy.
1st ed. 2017, X, 393 p. 11 illus., 4 illus. in color.
Hardcover
ISBN 978-3-319-55356-6
* Presents recent research in the area of diophantine number
theory and uniform distribution.
* Contains papers written by leading authorities in their fields.
* Dedicated to Robert F. Tichy on the occasion of his 60th birthday.
This volume is dedicated to Robert F. Tichy on the occasion of his 60th birthday.
Presenting 22 research and survey papers written by leading experts in their respective
fields, it focuses on areas that align with Tichy’s research interests and which he
significantly shaped, including Diophantine problems, asymptotic counting, uniform
distribution and discrepancy of sequences (in theory and application), dynamical systems,
prime numbers, and actuarial mathematics. Offering valuable insights into recent
developments in these areas, the book will be of interest to researchers and graduate
students engaged in number theory and its applications.
1st ed. 2017, X, 410 p. 27 illus., 15 illus. in color.
Hardcover
ISBN 978-3-319-52841-0
Series: Trends in Mathematics
* Features authoritative contributions
* Offers an intriguing outlook on future research directions
This volume consists of invited lecture notes, survey papers and original research papers
from the AAGADE school and conference held in B*dlewo, Poland in September 2015. The
contributions provide an overview of the current level of interaction between algebra,
geometry and analysis and demonstrate the manifold aspects of the theory of ordinary
and partial differential equations, while also pointing out the highly fruitful interrelations
between those aspects. These interactions continue to yield new developments, not only
in the theory of differential equations but also in several related areas of mathematics
and physics such as differential geometry, representation theory, number theory and
mathematical physics.
The main goal of the volume is to introduce basic concepts, techniques, detailed and
illustrative examples and theorems (in a manner suitable for non-specialists), and
to present recent developments in the field, together with open problems for more
advanced and experienced readers.
It will be of interest to graduate students, early-career researchers and specialists in
analysis, geometry, algebra and related areas, as well as anyone interested in learning new
methods and techniques.