Series: Universitext
2006, 370 p., Softcover
ISBN: 3-540-29020-6
Due: March 2006
About this textbook
In this revised and extended version of his course notes from a 1-year
course at Scuola Normale Superiore, Pisa, the author provides an
introduction ? for an audience knowing basic functional analysis
and measure theory but not necessarily probability theory ? to
analysis in a separable Hilbert space of infinite dimension.
Moreover, some details have been added as well as some new
material on dynamical systems with dissipative nonlinearities and
asymptotic behavior for gradient systems.
Table of contents
Gaussian Measures in Hilbert Spaces.- The Cameron-Martin Formula.-
Brownian Motion.- Stochastic Perturbations of a Dynamical System.-
Invariant Measures for Markov Semigroups.- Weak Convergence of
Measures.- Existence and Uniqueness of Invariant Measures.-
Examples of Markov Semigroups.- L2 Spaces with respect to a
Gaussian Measure.- Sobolev Spaces.- Gradient Systems.- Linear
Semigroups Theory.- Bibliography.
Series: Lecture Notes in Mathematics, Vol. 1873
2006, Approx. 120 p., Softcover
ISBN: 3-540-29407-4
Due: December 2, 2005
About this book
In November 2004, M. Yor and R. Mansuy jointly gave six lectures
at Columbia University, New York. These notes follow the contents
of that course, covering expansion of filtration formulae; BDG
inequalities up to any random time; martingales that vanish on
the zero set of Brownian motion; the Azema-Emery martingales and
chaos representation; the filtration of truncated Brownian
motion; attempts to characterize the Brownian filtration.
The book accordingly sets out to acquaint its readers with the
theory and main examples of enlargements of filtrations, of
either the initial or the progressive kind. It is accessible to
researchers and graduate students working in stochastic calculus
and excursion theory, and more broadly to mathematicians
acquainted with the basics of Brownian motion
Table of contents
Preliminaries.- Enlargements of Filtrations.- Stopping and Non-Stopping
Times.- On the Martingales which Vanish on the Set of Brownian
Zeroes.- PRP and CRP for some Remarkable Martingales.- Unveiling
the Brownian Path (or History) as the Level Rises.-Weak and
Strong Brownian Filtrations.- Appendix: Sketches of Solutions for
the Exercises.- References.- Index.
Series: CMS Books in Mathematics
2006, Approx. 320 p. 17 illus., Hardcover
ISBN: 0-387-28394-3
Due: December 2005
About this book
The theory of convex optimization has been constantly developing
over the past 30 years. Most recently, many researchers have been
studying more complicated classes of problems that still can be
studied by means of convex analysis, so-called "anticonvex"
and "convex-anticonvex" optimizaton problems. This
manuscript contains an exhaustive presentation of the duality for
these classes of problems and some of its generalization in the
framework of abstract convexity. This manuscript will be of great
interest for experts in this and related fields.
Table of contents
Preliminaries.- Worst approximation.- Duality for quasi-convex
supremization.- Optimal solutions for quasi-convex maximization.-
Reverse convex best approximation.- Unperturbational duality for
reverse convex infimization.- Optimal solutions for reverse
convex infimization.- Duality for d. c. optimization problems.-
Duality for optimization in the framework of abstract convexity.-
Notes and remarks.
Series: CMS Books in Mathematics
2006, Approx. 320 p. 46 illus., Hardcover
ISBN: 0-387-28719-1
Due: January 2006
About this textbook
This book deals with the study of convex functions and of their
behavior from the point of view of stability with respect to
perturbations. Convex functions are considered from the modern
point of view that underlines the geometrical aspect: thus a
function is defined as convex whenever its graph is a convex set.
A primary goal of this book is to study the problems of stability
and well-posedness, in the convex case. Stability means that the
basic parameters of a minimum problem do not vary much if we
slightly change the initial data. On the other hand, well-posedness
means that points with values close to the value of the problem
must be close to actual solutions. In studying this, one is
naturally led to consider perturbations of functions and of sets.
This approach fits perfectly with the idea of regarding functions
as sets. Thus the second part of the book starts with a short,
yet rather complete, overview of the so-called hypertopologies, i.e.
topologies in the closed subsets of a metric space.
While there exist numerous classic texts on the issue of
stability, there only exists one book on hypertopologies [Beer
1993]. The current book differs from Beerfs in that it contains
a much more condensed explication of hypertopologies and is
intended to help those not familiar with hypertopologies learn
how to use them in the context of optimization problems.
Table of contents
Preface.- Convex Sets and Convex Functions: the fundamentals.-
Continuity and Gamma (X).- The Derivatives and the
Subdifferential.- Minima and Quasi Minima.- The Fenchel Conjugate.-
Duality.- Linar Programming and Game Theory.- Hypertopologies,
Hyperconvergences.- Continuity of Some Operations Between
Functions.- Well-Posed Problems.- Generic Well-Posedness.- More
Exercises.- Appendix A: Functional Analysis.- Appendix B:
Topology.- Appendix C: More Game Theory.- Appendix D: Symbols,
Notations, Definitions and Important Theorems.- References, Index.
1. Edition - November 2005
2005. X, 206 Pages, Softcover
- Textbook -
ISBN 3-527-40610-7
Short description
This work meets the need for an affordable textbook on numerical
solutions of ODE. Carefully structured by an experienced textbook
author, it provides a survey of ODE for various applications,
both classical and modern.
From the contents
I Euler's Method
II Runge-Kutta Methods
III The Method of Taylor Expansions
IV Large Second Order Systems with Application to Nano Systems
V Completely Conservative, Covariant Numerical Methodology
VI Instability
VII Numerical Solution of Tridiagonal Linear Algebraic Systems
and Related Nonlinear Systems
VIII Approximate Solution of Boundary Value Problems
IX Special Relativistic Motion
X Special Topics
Appendix - Basic Matrix Operations
Bibliography