CBMS Regional Conference Series in Mathematics, Number: 110
2009; 85 pp; softcover
ISBN-13: 978-0-8218-4779-4
Expected publication date is May 13, 2009.
The Malliavin calculus was developed to provide a probabilistic proof of Hormander's hypoellipticity theorem. The theory has expanded to encompass other significant applications.
The main application of the Malliavin calculus is to establish the regularity of the probability distribution of functionals of an underlying Gaussian process. In this way, one can prove the existence and smoothness of the density for solutions of various stochastic differential equations. More recently, applications of the Malliavin calculus in areas such as stochastic calculus for fractional Brownian motion, central limit theorems for multiple stochastic integrals, and mathematical finance have emerged.
The first part of the book covers the basic results of the Malliavin calculus. The middle part establishes the existence and smoothness results that then lead to the proof of Hormander's hypoellipticity theorem. The last part discusses the recent developments for Brownian motion, central limit theorems, and mathematical finance.
Graduate students and research mathematicians interested in probability, the Malliavin calculus, and stochastic partial differential equations.
American Mathematical Society Translations--Series 2, Volume: 226
2009; approx. 269 pp; hardcover
ISBN-13: 978-0-8218-4801-2
Expected publication date is June 20, 2009.
The volume consists of articles by friends and collaborators of a renowned Russian mathematician V. P. Havin, prepared on the occasion of Havin's 75th birthday. The articles in the volume are devoted to areas of analysis where Havin himself worked successfully for many years.
Graduate students and research mathematicians interested in analysis.
A. Aleman and C. Sundberg -- Zeros of functions in weighted Bergman spaces
S. Alesker, S. Artstein-Avidan, and V. Milman -- A characterizataion of the Fourier transform and related topics
J. Bourgain -- Geodesic restrictions and L^p-estimates for eigenfunctions of Riemannian surfaces
S. Favorov and L. Golinskii -- A Blaschke-type condition for analytic and subharmonic functions and application to contraction operators
A. Fryntov and L. Nazarov -- New estimates for the length of the Erd?s-Herzog-Piranian lemniscate
P. M. Gauthier and M. S. Melnikov -- Compact approximation by bounded functions and functions continuous up to the boundary
J.-P. Kahane -- Un theoreme de Helson pour des series de Walsh
X. Massaneda and J. Ortega-Cerda -- Interpolation sequences for the Bernstein algebra
V. Maz'ya -- Integral and isocapacitary inequalities
V. V. Peller -- Differentiability of functions of contractions
A. Poltoratski -- Asymptotic behavior of arguments of Cauchy integrals
D. Sarason -- Free interpolation in the Nevanlinna class
K. Seip -- Interpolation by Dirichlet series in H^infty
M. Solomyak -- Remarks on counting negative eigenvalues of the Schrodinger operator on regular metric trees
S. Treil -- H^1 and dyadic H^1
V. Vasyunin and A. Volberg -- Monge-Ampere equation and Bellman optimization of Carleson embedding theorems
A. Volberg and P. Yuditskii -- Remarks on Nehari's problem, matrix A_2 condition
American Mathematical Society Translations--Series 2, Volume: 227
2009; approx. 272 pp; hardcover
ISBN-13: 978-0-8218-4821-0
Expected publication date is July 17, 2009.
This volume contains translations of papers that originally appeared in the Japanese journal S?gaku. The papers range over a variety of topics in probability theory, statistics, and applications.
This volume is suitable for graduate students and research mathematicians interested in probability and statistics.
Graduate students and research mathematicians interested in probability and statistics.
J. Akahori, M. Izumi, and S. Watanabe -- Noises, stochastic flows and $E_O$-semigroups
S. Kuriki and A. Takemura -- Volume of tubes and distribution of the maxima of Gaussian random fields
T. Funaki -- Stochastic analysis on large scale interacting systems
T. Mikami -- Optimal transportation problem as stochastic mechanics
M. Hayashi -- Quantum estimation and the quantum central limit theorem
S. Aoki and A. Takemura -- Statistics and Grobner bases-The origin and development of computational algebraic statistics
S. Tomizawa -- Analysis of square contingency tables in statistics
M. Akahira -- The structure of higher order asymptotic theory of statistical estimation
A. Takahashi -- On an asymptotic expansion approach to numerical problems in finance
K. Kuroda and N. Matsuyama -- Actuarial mathematics: Theory and current practice in Japan
Contemporary Mathematics, Volume: 485
2009; 162 pp; softcover
ISBN-13: 978-0-8218-4649-0
Expected publication date is June 13, 2009. Suggest to a Colleague This book contains papers written by participants at the two Chapel Hill Ergodic Theory Workshops organized in February 2007 and 2008. The topics covered by these papers help to illustrate the interaction between ergodic theory and related fields such as harmonic analysis, number and probability theories.
Readership
Graduate students and research mathematicians interested in ergodic theory and probability theory.
Contemporary Mathematics, Volume: 486
2009; 383 pp; softcover
ISBN-13: 978-0-8218-4279-9
Expected publication date is June 14, 2009.
The purpose of this collection is to guide the non-specialist through the basic theory of various generalizations of topology, starting with clear motivations for their introduction. Structures considered include closure spaces, convergence spaces, proximity spaces, quasi-uniform spaces, merotopic spaces, nearness and filter spaces, semi-uniform convergence spaces, and approach spaces. Each chapter is self-contained and accessible to the graduate student, and focuses on motivations to introduce the generalization of topologies considered, presenting examples where desirable properties are not present in the realm of topologies and the problem is remedied in the more general context. Then, enough material will be covered to prepare the reader for more advanced papers on the topic. While category theory is not the focus of the book, it is a convenient language to study these structures and, while kept as a tool rather than an object of study, will be used throughout the book. For this reason, the book contains an introductory chapter on categorical topology.
Readership
Graduate students and research mathematicians interested in topology, geometry, analysis, and the foundations of mathematics.