This book collects some recent developments in stochastic control theory with applications to financial mathematics. We first address standard stochastic control problems from the viewpoint of the recently developed weak dynamic programming principle. A special emphasis is put on the regularity issues and, in particular, on the behavior of the value function near the boundary. We then provide a quick review of the main tools from viscosity solutions which allow to overcome all regularity problems. We next address the class of stochastic target problems which extends in a nontrivial way...
This book collects some recent developments in stochastic control theory with applications to financial mathematics. We first address standard ...
Inner functions form an important subclass of bounded analytic functions. Since they have unimodular boundary values, they appear in many extremal problems of complex analysis. They have been extensively studied since early last century, and the literature on this topic is vast. Therefore, this book is devoted to a concise study of derivatives of these objects, and confined to treating the integral means of derivatives and presenting a comprehensive list of results on Hardy and Bergman means. The goal is to provide rapid access to the frontiers of research in this field. This monograph will...
Inner functions form an important subclass of bounded analytic functions. Since they have unimodular boundary values, they appear in many extremal pro...
This book addresses the need for an accessible comprehensive exposition of the theory of uniform measures; the need that became more critical when recently uniform measures reemerged in new results in abstract harmonic analysis. Until now, results about uniform measures have been scattered through many papers written by a number of authors, some unpublished, written using a variety of definitions and notations. Uniform measures are certain functionals on the space of bounded uniformly continuous functions on a uniform space. They are a common generalization of several classes of...
This book addresses the need for an accessible comprehensive exposition of the theory of uniform measures; the need that became more critical w...
This monograph gives a short introduction to the relevant modern parts of discrete geometry, in addition to leading the reader to the frontiers of geometric research on sphere arrangements. The readership is aimed at advanced undergraduate and early graduate students, as well as interested researchers. It contains more than 40 open research problems ideal for graduate students and researchers in mathematics and computer science. Additionally, this book may be considered ideal for a one-semester advanced undergraduate or graduate level course.
The core part of this book is...
This monograph gives a short introduction to the relevant modern parts of discrete geometry, in addition to leading the reader to the frontiers of ...
This book gives an introduction to the very active field of combinatorics of affine Schubert calculus, explains the current state of the art, and states the current open problems. Affine Schubert calculus lies at the crossroads of combinatorics, geometry, and representation theory. Its modern development is motivated by two seemingly unrelated directions. One is the introduction of k-Schur functions in the study of Macdonald polynomial positivity, a mostly combinatorial branch of symmetric function theory. The other direction is the study of the Schubert bases of the (co)homology of the...
This book gives an introduction to the very active field of combinatorics of affine Schubert calculus, explains the current state of the art, and s...
This volumepresents a lively introduction to the rapidly developing and vast research areas surroundingCalabi Yau varieties and string theory.With its coverage of the various perspectives of a wide area of topics such as Hodge theory, Gross Siebert program, moduli problems, toric approach, and arithmetic aspects, the book gives a comprehensive overview of the current streams of mathematical research in the area.
The contributions in this book are basedon lectures that took place during workshops with the following thematictitles: Modular Forms Around String Theory,...
This volumepresents a lively introduction to the rapidly developing and vast research areas surroundingCalabi Yau varieties and string theory.With ...
This book gives an introduction to the very active field of combinatorics of affine Schubert calculus, explains the current state of the art, and states the current open problems. Affine Schubert calculus lies at the crossroads of combinatorics, geometry, and representation theory. Its modern development is motivated by two seemingly unrelated directions. One is the introduction of k-Schur functions in the study of Macdonald polynomial positivity, a mostly combinatorial branch of symmetric function theory. The other direction is the study of the Schubert bases of the (co)homology of the...
This book gives an introduction to the very active field of combinatorics of affine Schubert calculus, explains the current state of the art, and s...
This book deals with a systematic study of a dynamical system approach to investigate the symmetrization and stabilization properties of nonnegative solutions of nonlinear elliptic problems in asymptotically symmetric unbounded domains.
This book deals with a systematic study of a dynamical system approach to investigate the symmetrization and stabilization properties of nonnegative s...
