Book
Oct 2025
Discusses limit theorems for Toeplitz and tapered Toeplitz-type random quadratic functionals of stationary processes
Addresses statistical inference problems related to the spectra of the observed processes
Presents a unified treatment of the trace approximation problem for Toeplitz matrices and operators
Part of the book series: Frontiers in Probability and the Statistical Sciences (FROPROSTAS)
This book presents recent findings on central and non-central limit theorems for Toeplitz and tapered Toeplitz random quadratic functionals of stationary processes, with applications in spectral-based statistical inference. It focuses on Gaussian, orthogonal increment-driven, and Lévy-driven linear stationary processes with memory, in both discrete and continuous time.
Toeplitz matrices and operators are central to the study of stationary processes. The covariance matrix of a discrete-time stationary process is a truncated Toeplitz matrix generated by the process's spectral density; in continuous-time, this becomes a Toeplitz operator. The foundations of the trace approximation problem were laid by Grenander and Szegö in their classical monograph “Toeplitz Forms and Their Applications” (1958), and the subject has recently seen renewed interest due to developments in long-range dependence and tapered data analysis.
The book addresses topics that are often overlooked in other texts, including the trace approximation problem, central limit theorems in continuous time, functional central and non-central limit theorems for Toeplitz processes, and central limit theorems for tapered functionals. It also covers approaches to estimating linear and nonlinear spectral functionals, Whittle estimators, and goodness-of-fit tests using tapered data – each enriched by new advances in the field.
Comprising ten chapters and two appendices, the book begins with an overview of the main problems and a review of foundational concepts from real analysis, functional analysis, and matrix analysis. It then introduces a model that is a second-order stationary process and discusses key concepts and results from the general theory of stationary processes, before delving into the trace approximation problem. Subsequent chapters cover central and non-central limit theorems for Toeplitz and tapered Toeplitz random quadratic functionals and explore statistical inference problems. The appendices discuss the motivations and benefits of data tapering, and outline several important problems closely related to the main themes of the book.
The text will be a valuable resource for researchers in time series analysis, econometrics, finance, and applied statistics. It is suitable for graduate-level courses in time series analysis or the statistics of stochastic processes, and as a supplementary reference for students of advanced statistics, probability, econometrics, or finance.
Conference proceedings
Nov 2025
A collection of 10 timely research contributions by top-level specialists in Complex and Algebraic Geometry
Covers a wide array of modern research directions in Hodge theory
Develops new and original viewpoints on the structure and compactifications of moduli spaces
Part of the book series: Simons Symposia (SISY)
This book brings together contributions by top-level experts from a wide range of topics in modern Hodge theory, originating in the authors’ participation in the special years on Hodge theory at the Institute of Mathematical Sciences of the Americas (IMSA) in Miami.
One of the main themes is the study of moduli spaces and their compactifications. Several articles speak of the singularities occuring in the boundaries of geometrical or Hodge-theoretic compactifications, semistable reduction, the implications of canonical models for model theory in the sense of logic, and fundamental groups of moduli spaces and their associated Torelli groups. Other topics include Mukai lattices, derived moduli spaces, foliations, Higgs bundles and hyperbolicity, the study of pseudoconvexity properties of neighborhoods of infinity, contributions to the theory of degenerations and limiting mixed Hodge structures.
This text will provide an indispensable reference for research mathematicians and specialist graduate students, where the modern approaches to moduli spaces are illustrated by their realizations and applications in examples of interest for the interplay between Hodge theory and moduli spaces.
Book
Oct 2025
Gives recursive computationally explicit estimators and adaptive filters for five models of partially observed systems
The proposed adaptive filters are asymptotically (small noise, large samples) efficient in the minimax sense
The construction of continuous and discrete time adaptive filters admits generalization to other models
Part of the book series: Springer Series in Statistics (SSS)
This book is devoted to the problem of adaptive filtering for partially observed systems depending on unknown parameters. Adaptive filters are proposed for a wide variety of models: Gaussian and conditionally Gaussian linear models of diffusion processes; some nonlinear models; telegraph signals in white Gaussian noise (all in continuous time); and autoregressive processes observed in white noise (discrete time). The properties of the estimators and adaptive filters are described in the asymptotics of small noise or large samples. The parameter estimators and adaptive filters have a recursive structure which makes their numerical realization relatively simple. The question of the asymptotic efficiency of the adaptive filters is also discussed.
Readers will learn how to construct Le Cam’s One-step MLE for all these models and how this estimator can be transformed into an asymptotically efficient estimator process which has a recursive structure.
The last chapter covers several applications of the developed method to such problems as localization of fixed and moving sources on the plane by observations registered by K detectors, estimation of a signal in noise, identification of a security price process, change point problems for partially observed systems, and approximation of the solution of BSDEs.
Adaptive filters are presented for the simplest one-dimensional observations and state equations, known initial values, non-correlated noises, etc. However, the proposed constructions can be extended to a wider class of models, and the One-step MLE-processes can be used in many other problems where the recursive evolution of estimators is an important property.
The book will be useful for students of filtering theory, both undergraduates (discrete time models) and postgraduates (continuous time models). The method described, preliminary estimator + One-step MLE-process + adaptive filter, will also be of interest to engineers and researchers working with partially observed models.
Book
Nov 2025
Focuses on the study of the global properties of the dynamical systems
Gives a justification of using numerical methods for solving several mathematical problems
Targets researchers in dynamical systems in engineering, physics, chemistry, biology, economics, and demography
Part of the book series: Mathematical Marvels: Texts and Monographs in the Spirit of CR Rao (MMCRR)
This book is devoted to the study of the global properties of the dynamical systems. It gives a justification of using numerical methods for solving several problems such as localization of a chain-recurrent set of trajectories, construction of attractors and their domains of attraction, construction of filtrations, calculation of invariant measures, approximation of ergodic measures, estimation of the entropy of a dynamical system, calculation of the averaging spectrum of a function, calculation of the Morse spectrum, a test for the hyperbolicity of a dynamical system. The book is intended for researchers in dynamical systems and their applications in many scientific and technical disciplines, including engineering, physics, chemistry, biology, economics, and demography.
Book
Oct 2025
Celebrates Prof. Dajczer's contributions and influence in the development of research on this topic
Gathers selected contributions from his mathematical descendants across four continents
Features in-depth discussions on relevant topics in the field
Part of the book series: Latin American Mathematics Series (LAMS)
Part of the book sub series: Latin American Mathematics Series – UFSCar subseries (LAMSUFSC)
This contributed volume collects articles by specialists in submanifold theory, geometric analysis, and Riemannian geometry, with contributors from four continents. It is dedicated to Professor Marcos Dajczer, whose research and teaching activities have influenced new generations of geometers. Some of the works contained in this volume are written by his mathematical descendants and reflect the state of the art and current discussion in the field.
Now retired from the Institute of Pure and Applied Mathematics (IMPA), Brazil, but still active, Professor Dajczer has conducted research in these and other fields, contributing to the development of submanifold theory in Brazil. He completed his undergraduate studies at the University of Buenos Aires, Argentina, in 1975, and received his PhD in Mathematics from IMPA in 1980. A postdoctoral period at the State University of New York in Stony Brook marked the beginning of a fruitful collaboration with Prof. D. Gromoll that lasted several years.
Prof. Dajczer and Dr. Ruy Tojeiro are co-authors of the textbook Submanifold Theory: Beyond an Introduction, which is available in Springer's Universitext series.
Book
Oct 2025
Features lecture notes, surveys, and original research, ideal for pedagogical use independently or in the classroom
Illustrates the power of geometric methods in understanding complex physical systems
Progresses from foundational mathematical structures to concrete applications
Part of the book series: Tutorials, Schools, and Workshops in the Mathematical Sciences (TSWMS)
This book presents selected lectures from the Wisła 22 Winter School and Workshop organized by the Baltic Institute of Mathematics that illustrate the power of geometric methods in understanding complex physical systems. Chapters progress from foundational mathematical structures to concrete applications in fluid dynamics and mechanical systems, highlighting the profound connection between differential geometry and physical phenomena.
The first chapter investigates differentiable structures on a non-Hausdorff line with two origins, setting the stage for the applications that follow. The next chapter transitions to fluid mechanics through a study of generalized geometry in two-dimensional incompressible fluid flows, establishing the mathematical framework needed for analyzing fluid systems through geometric lenses. Building on these foundations, the third chapter expands the perspective with a comprehensive treatment of nonlinear differential equations in fluid mechanics, utilizing concepts from contact and symplectic geometry to illuminate singular properties of fluid dynamics solutions. Finally, the fourth chapter demonstrates how geometric methods extend beyond fluid mechanics to mechanical systems with nonholonomic constraints, revealing how geometric formulations can address challenging phenomena like discontinuities, collisions, and the counterintuitive stabilization of inverted pendulums.
Geometric Methods in Physical Systems is ideal for graduate students and researchers working in these areas. A basic understanding of differential geometry and mathematical analysis is assumed.
Book
Nov 2025
Discusses topics on the Fourier transform, Hankel transform, Weinstein transform, and pseudo-differential operators
Highlights the study of the theory of pseudo-differential operators involving the Weinstein transform
Explains the application of the Weinstein transform, which has a rich calculus, in many areas of mathematical sciences
Part of the book series: Industrial and Applied Mathematics (INAMA)
This book discusses topics on the Fourier transform, Hankel transform, Weinstein transform, and pseudo-differential operators. Targeted to researchers and graduate students, it is useful in the study of the theory of pseudo-differential operators involving the Weinstein transform. This book is also helpful in the study of partial differential equations, wavelet analysis, harmonic analysis, and functional analysis. Throughout the book, the reader is assumed to have an understanding of the basics of real analysis and functional analysis. The Weinstein transform whose kernel consists of a complex exponential function and a normalized Bessel function of the first kind. The Weinstein transform has a rich calculus and can be applied in many areas of mathematical sciences. Pseudo-differential operators are the generalization of partial differential operators, and they play a significant role in the problems of partial differential equations, numerical analysis, and quantum physics.