Series: Lecture Notes in Mathematics
Subseries: Seminaire de Probabilites , Vol. 1899
2007, Approx. 480 p., Softcover
ISBN: 978-3-540-71188-9
About this book
Two noteworthy features of the 40th volume of Seminaire de
Probabilites are L. Coutinfs advanced course on calculus driven
by fractional Brownian motion, and a series of seven interrelated
works on local time-space calculus. Other topics from stochastic
processes and stochastic finance include three contributions by A.S.
Cherny on general approaches to arbitrage pricing.
Table of contents
Preface.- Specialized Course. Laure Coutin: An introduction to (stochastic)
calculus with respect to fractional Brownian motion.- Local Time-Space
Calculus. G. Peskir: A change-of-variable formula with local time
on surfaces.- A. E. Kyprianou, B.A. Surya: A note on a change of
variable formula with local time-space for Levy processes of
bounded variation.- J. Najnudel: Integration with respect to
local time and selfintersection of local time of a one-dimensional
Brownian motion.- D. Elworthy, A. Truman, H. Zhao: Generalized
Ito formulae and space-time Lebesgue-Stieltjes integrals of local
time.- N. Eisenbaum: Local time-space calculus for reversible
semimartingales.- F. Russo, P. Vallois: Elements of stochastic
calculus via regularisation.- H. Pham: On the smooth-fit property
for one-dimensional optimal switching problem.- Other
contributions. I. Crimaldi, G. Letta, L. Pratelli: A strong form
of stable convergence.- P. J. Catuogno, P. R. C. Ruffino: Product
of harmonic maps is harmonic: a stochastic approach.- M. Ledoux:
More Hypercontractive Bounds for Deformed Orthogonal Polynomial
Ensembles.- E. Cepa, D. Lepingle: No multiple collisions for
mutually repelling Brownian particles.- L. Alili, P. Patie: On
the joint law of the L1 and L2 norms of a 3-dimensional Bessel
bridge.- P. Salminen, M. Yor: Tanaka formula for symmetric Levy
processes.- M. Pistorius: An excursion theoretical approach to
some boundary crossing problems and the Skorokhod embedding for
reflected Levy processes.- J. Obloj: The maximality principle
revisited: on certain optimal stopping problems.- N. Enriquez:
Correlated processes and the composition of generators.- L.
Serlet: Representation of the martingales for the Brownian snake.-
E. Gobet, S.Menozzi: Discrete sampling of functionals of Ito
processes.- O. Chybriakov: Itofs integrated formula for strict
local martingales with jumps.- S. Ankirchner, S. Dereich, P.
Imkeller: Enlargement of filtrations and continuous Girsanov-type
embeddings.- M. De Donno, M. Pratelli: On a lemma by Ansel and
Stricker.- A.S. Cherny: General arbitrage pricing model: I.Probability
approach.- II.Transaction costs.- III.Possibility approach.
Series: Lecture Notes in Mathematics , Vol. 1906
2007, XIII, 198 p., Softcover
ISBN: 978-3-540-71226-8
About this book
Inverse problems arise whenever one tries to calculate a required
quantity from given measurements of a second quantity that is
associated to the first one. Besides medical imaging and non-destructive
testing, inverse problems also play an increasing role in other
disciplines such as industrial and financial mathematics. Hence,
there is a need for stable and efficient solvers. The book is
concerned with the method of approximate inverse which is a
regularization technique for stably solving inverse problems in
various settings such as L2-spaces, Hilbert spaces or spaces of
distributions. The performance and functionality of the method is
demonstrated on several examples from medical imaging and non-destructive
testing such as computerized tomography, Doppler tomography,
SONAR, X-ray diffractometry and thermoacoustic computerized
tomography. The book addresses graduate students and researchers
interested in the numerical analysis of inverse problems and
regularization techniques or in efficient solvers for the
applications mentioned above.
Table of contents
Part I: Inverse and Semi-discrete Problems: Ill-posed Problems
and Regularization Methods.- Approximate Inverse in L2-spaces.-
Approximate Inverse in Hilbert Spaces.- Approximate Inverse in
Distribution Spaces.- Conclusion and Perspectives.- Part II:
Application to 3D Doppler Tomography.- A Semi-discrete Setup for
Doppler Tomography.- Solving the Semi-discrete Problem.-
Convergence and Stability.- Approaches for Defect correction.-
Conclusion and Perspectives.- Part III: Application to the
Spherical mean operator.- The Spherical Mean Operator.- Design of
a Mollifier.- Computation of Reconstruction Kernels.- Numerical
Experiments.- Conclusion and Perspectives.- Part IV: Further
Applications.- Approximate Inverse and X-ray Diffractometry.- A
Filtered Backprojection Algorithm for Thermoacoustic Computerized
Tomography (TCT).- Computation of Reconstruction Kernels in 3D
Computerized Tomography.- Conclusion and Perspectives.-
References.- Index.
Series: Springer Optimization and Its Applications , Vol. 8
2007, Approx. 300 p., Hardcover
ISBN: 978-0-387-69755-0
About this textbook
This book gives a clear presentation of set-valued analysis and
monotone operators and also presents several important new
results in the field. The first part of the book begins with a
self-contained and encompassing overview of several key topics
within set-valued analysis. The authors present basic notions of
set convergence, and of continuity of set-valued mappings,
together with the many important results in infinite-dimensional
convex analysis, leading to the classical fixed point results due
to Ekeland, Caristi and Kakutani. Next, an in-depth introduction
to monotone operators is developed, emphasizing results related
to maximality of subdifferentials and of sums of monotone
operators.
The second part of the monograph contains new results, all of
them established during the last decade, on a concept of
enlargements of monotone operators, which is then applied to
several fields of interest in applied mathematcs like bundle-type
methods, augmented Lagrangian methods or variational inequalities
and recently developed versions of proximal point algorithms. The
results in the second part use extensively the concepts presented
in the first one.
The unique features of the book include the previously
unpublished contents of chapters 5?6, as well as the presentation
of the results in chapters 1?4, which are at the same time
accessible, self contained, and hold at a high level of
generality.
All the concepts and practically all proofs are given within the
text, so that a wide audience can have a friendly, but at the
same time deep, access to many of the most relevant topics set-valued
analysis.
Table of contents
Preface.- 1. Introduction.- 2. Set Convergence and Point-to-Set
Mappings.- 3. Convex Analysis and Fixed Point Theorems.- 4.
Maximal Monotone Operators.- 5. Enlargements of Monotone
Operators.- 6. Recent Topics in Proximal Theory.- Bibliography.-
Index.
Series: Springer Texts in Statistics
2007, Approx. 540 p., Hardcover
ISBN: 978-0-387-70872-0
About this textbook
Matrix algebra is one of the most important areas of mathematics
for data analysis and for statistical theory. The first part of
this book presents the relevant aspects of the theory of matrix
algebra for applications in statistics. This part begins with the
fundamental concepts of vectors and vector spaces, next covers
the basic algebraic properties of matrices, then describes the
analytic properties of vectors and matrices in the multivariate
calculus, and finally discusses operations on matrices in
solutions of linear systems and in eigenanalysis. This part is
essentially self-contained
Table of contents
Basic vector/matrix structure and notation.-Vectors and vector
spaces.- Basic properties of matrices.- Vector/matrix derivatives
and integrals.- Matrix tranformations and factorizations.-
Solution of linear systems.- Evaluation of Eigenvalues and
Eigenvectors.- Special matrices and operations useful in modeling
and data analysis.- Selected applications in statistics.-
Numerical methods.- Numerical linear algebra.- Software for
numerical linear algebra.
Series: Springer Series in Statistics
2007, Approx. 260 p., Hardcover
ISBN: 978-0-387-70778-5
About this book
Following the classical sampling theory, the survey statistician
selects samples of people, businesses or others, in order to
obtain the desired information. Drawing the samples is usually
done by randomly selecting from a list representing the target
population. In practice, this list is often not available. At
best, the statistician only has access to a different list,
indirectly related to the targeted population.
The example of a survey of children where the statistician only
has a list of adult persons is a typical case. In this case, the
statistician first draws a sample of adults, and for each
selected adult, the statistician then identifies his/her children.
The survey is done from the latter. This is what is called
indirect sampling.
When indirect sampling is used jointly with the sampling of
clusters of persons (families, for example), many complications
arise for the survey statistician. One of the complications
relates to the computation of the estimates from the survey. The
production of estimates of simple totals or means can then become
nightmares for the survey statistician. To solve this problem,
the author proposes a simple solution, easy to implement, that is
called the generalised weight share method.
This book is the reference on indirect sampling and the
generalised weight share method. It contains the different
developments done by the author on these subjects. The theory
surrounding them is presented, but also different possible
applications that drive its interest. The reader will find in
this book the answer to questions that come, inevitably, when
working in a context of indirect sampling.
Table of contents
Introduction.- Description and use of the GWSM.- Literature
review.- Properties.- Other generalisations.- Application to
longitudinal surveys.- GWSM and calibration.- Non-response.- GWSM
and record linkage.- Conclusion.
Series: Graduate Texts in Mathematics
2007, Approx. 400 p., 40 illus., Hardcover
ISBN: 978-0-387-70998-7
About this textbook
A central problem in additive number theory is the growth of
sumsets. If A is a finite or infinite subset of the integers and
the lattice points, or more generally, of any abelian group or
semigroup G, then the h-fold sumset of A is the set LA consisting
of all elements of G that can be represented as the sum of L not
necessarily distinct elements of A. The goal is to understand the
asymptotics of the sumsets LA , that is, the size and structure
of LA, as L tends to infinity. If A is finite, then the size of
LA is its cardinality. If A is infinite, then the size of LA is
measured by various duality functions. These problems have
natural analogues when A is a subset of a nonabelian group.
Additive Number Theory: Density Theorems and the Growth of
Sumsets presents material that deals with the above problem.
Ideas and techniques from many parts of mathematics are used to
prove theorems in this subject. For example, the authors use
number theory, combinatorics, commutative algebra, ultrafilters
and logic, and nonstandard analysis. The book is self-contained,
and includes short introductions to the various techniques that
are not standard in this field.
Table of contents
Preface.- Part I. Sums of finite sets of integers.- Part II. Sums
of finite sets of lattice points.- Part II. Ehrhart polynomials.-
Part IV. Geometric group theory.- Part V. Schnirelmann density
and applications.- Part VI. Asymptotic density.- Part VII. Kneser
Theorems and applications.- Part VIII. Bilufs Theorem.- Part IX.
Ultrafilters and Hindmanfs Theorem.- Part X. Nonstandard
Analysis.- Part XI. Upper Banach density problems and Renling Jinfs
results.- Index
Series: Springer Monographs in Mathematics
2008, Approx. 300 p., Hardcover
ISBN: 978-1-84628-851-7
About this book
The use of various types of wave energy is an increasingly
promising, non-destructive means of detecting objects and of
diagnosing the properties of quite complicated materials. An
analysis of this technique requires an understanding of how waves
evolve in the medium of interest and how they are scattered by
inhomogeneities in the medium. These scattering phenomena can be
thought of as arising from some perturbation of a given, known
system and they are analysed by developing a scattering theory.
This monograph provides an introductory account of scattering
phenomena and a guide to the technical requirements for
investigating wave scattering problems. It gathers together the
principal mathematical topics which are required when dealing
with wave propagation and scattering problems, and indicates how
to use the material to develop the required solutions.
Both potential and target scattering phenomena are investigated
and extensions of the theory to the electromagnetic and elastic
fields are provided. Throughout, the emphasis is on concepts and
results rather than on the fine detail of proof; a bibliography
at the end of each chapter points the interested reader to more
detailed proofs of the theorems and suggests directions for
further reading.
Aimed at graduate and postgraduate students and researchers in
mathematics and the applied sciences, this book aims to provide
the newcomer to the field with a unified, and reasonably self-contained,
introduction to an exciting research area and, for the more
experienced reader, a source of information and techniques.
Table of contents
Introduction and Outline of Contents.- Some One-dimensional
Examples.- Preliminary Mathematical Material.- Concerning Hilbert
Spaces.- Two Important Techniques.- A Scattering Theory Strategy.-
An Approach to Echo Analysis.- Scattering Processes in Stratified
Media.- Scattering in Spatially Periodic Media.- On Inverse
Problems.- Scattering in other Wave Systems.- Commentary.-
Bibliography