Format: Paperback / softback, 118 pages, height x width: 235x155 mm, 24 Illustrations, color;
18 Illustrations, black and white; X, 118 p. 42 illus., 24 illus. in color., 1
Series: SpringerBriefs in Statistics
Pub. Date: 01-Apr-2025
ISBN-13: 9789819608812
In this book, we explain the development of a new filtering method to estimate the hidden states of random variables for multiple non-stationary time series data. This method is particularly helpful in analyzing small-sample non-stationary macro-economic time series. The method is based on the frequency-domain application of the separating information maximum likelihood (SIML) method, which was proposed by Kunitomo, Sato, and Kurisu (Springer, 2018) for financial high-frequency time series. We solve the filtering problem of hidden random variables of trend-cycle, seasonal, and measurement-error components and propose a method to handle macro-economic time series. The asymptotic theory based on the frequency-domain analysis for non-stationary time series is developed with illustrative applications, including properties of the method of Muller and Watson (2018), and analyses of macro-economic data in Japan.
Vast research has been carried out on the use of statistical time series analysis for macro-economic time series. One important feature of the series, which is different from standard statistical time series analysis, is that the observed time series is an apparent mixture of non-stationary and stationary components. We apply the SIML method for estimating the non-stationary errors-in-variables models. As well, we discuss the asymptotic and finite sample properties of the estimation of unknown parameters in the statistical models. Finally, we utilize their results to solve the filtering problem of hidden random variables and to show that they lead to new a way to handle macro-economic time series.
Introduction.- Macro Examples and Non-Stationary Errors-in-Variables
Model.- The SIML Filtering Method.- Comparing Estimation Methods of
Non-stationary Errors-in Variables Models.- Frequency Regression and
Smoothing for Noisy Non-stationary Multivariate Time Series.
Format: Paperback / softback, 245 pages, height x width: 235x155 mm,
182 Illustrations, black and white; XII, 245 p. 182 illus.,
Series: Compact Textbooks in Mathematics
Pub. Date: 16-Mar-2025
ISBN-13: 9783662706015
This book serves as an introduction to topology, a branch of mathematics that studies the qualitative properties of geometric objects. It is designed as a bridge between elementary courses in analysis and linear algebra and more advanced classes in algebraic and geometric topology, making it particularly suitable for both undergraduate and graduate mathematics students. Additionally, it can be used for self-study.
The authors employ the modern language of category theory to unify and clarify the concepts presented, with definitions supported by numerous examples and illustrations. The book includes over 170 exercises that reinforce and deepen the understanding of the material. Many sections feature brief insights into advanced topics, providing a foundation for study projects or seminar presentations.
In addition to set-theoretic topology, the book covers essential concepts such as fundamental groups, covering spaces, bundles, sheaves, and simplicial methods, which are vital in contemporary geometry and topology.
Basic Concepts of Topology.- Universal Constructions.- Connectivity and Separation.- Compactness and Mapping Spaces.- Transformation Groups.- Paths and Loops.- The Fundamental Group.- Covering Spaces.- Bundles and Fibrations.- Sheaves.- Simplicial Sets.
Format: Paperback / softback, 150 pages, height x width: 235x155 mm, 2 Illustrations, color;
1 Illustrations, black and white; XI, 150 p. 3 illus., 2 illus. in color.
Series: SpringerBriefs on PDEs and Data Science
Pub. Date: 23-Mar-2025
ISBN-13: 9789819618965
This book characterizes the open-loop and closed-loop solvability for time-delayed linear quadratic optimal control problems. Different from the existing literature, in the current book, we present a theory of deterministic LQ problems with delays which has several new features:
Our system is time-varying, with both the state equation and cost functional being allowed to include discrete and distributed delays, both in the state and the control. We take different approaches to discuss the unboundedness of the control operator.
The open-loop solvability of the lifted problem is characterized by the solvability of a system of forward-backward integral evolution equations and the convexity condition of the cost functional. Surprisingly, the adjoint equations involve some coupled partial differential equations, which is significantly different from that in the literature, where, the adjoint equations are all some anticipated backward ordinary differential equations.
The closed-loop solvability is characterized by the solvability of three equivalent integral operator-valued Riccati equations and two equivalent backward integral evolution equations which are much easier to handle than the differential operator-valued Riccati equations used in the literature to study similar problems.
The closed-loop representation of open-loop optimal control is presented through three equivalent integral operator-valued Riccati equations.
Chapter 1 Introduction.
Chapter 2 Problem Lifting.-
Chapter 3 Solutions to the LQ Problems.
Format: Hardback, 286 pages, height x width: 235x155 mm, 16 Illustrations, black and white; XII, 286 p. 16 illus.,
Pub. Date: 27-Dec-2024
This textbook provides an accessible approach to concepts and applications of stochastic processes ideal for a wide range of readers. This revised third edition features an intuitive reorganization with concrete topics introduced early on which are then used to demonstrate more abstract concepts in later chapters. The author has kept chapters short and independent from each other, with several of the longer chapters from previous editions now divided into smaller, more manageable parts. These changes build upon previous editions to allow readers even greater flexibility.
The applications that are covered feature active areas of research within biological modeling, such as cancerous mutations, influenza evolution, drug resistance, and immune response. Important problems in fields such as engineering and mathematical physics are presented as well. These topics elegantly apply various classical stochastic models and are motivated throughout with many worked out examples.
This third edition of Classical and Spatial Stochastic Processes is suitable as a textbook for a first course in stochastic processes at the upper-undergraduate or graduate level. Because of its accessible approach, it may also be used as a self-study resource for researchers and practitioners in mathematics, engineering, physics, and mathematical biology.
Finite Markov Chains.- Random walks on finite graphs.- The first
appearance of a pattern.- The ruin problem.- The Ehrenfest chain.- The simple
symmetric random walk.- Asymmetric and higher dimension random
walks.- Discrete time birth and death chains.- Discrete time branching
process.- Recurrence on countable spaces.- Stationary distributions on
countable spaces.- The Poisson process.- Continuous time birth and death
chains.- Continuous time branching processes.- Percolation.- A cellular
automaton.- A branching random walk.- The contact process on a homogeneous
tree.- Appendix: A little more probability.- Bibliography.- Index.
Format: Hardback, 301 pages, height x width: 235x155 mm, 22 Illustrations, color;
9 Illustrations, black and white; XIII, 301 p. 31 illus., 22 illus. in color.,
Series: Trends in Mathematics
Pub. Date: 20-Apr-2025
ISBN-13: 9783031804526
This volume provides readers with an overview of the most recent developments in the mathematical fields related to fractals. It includes both original research contributions, as well as surveys from many of the leading experts on modern fractal geometry theory and applications. The contributions contained in the book stem from the conference Fractals and Related Fields IV", that was held in 2022 on the Island of Porquerolles, France. Various aspects of fractal geometry in connection with harmonic analysis, geometric measure theory, ergodic theory and dynamical systems, probability theory, number theory, functional analysis, additive combinatorics, embedding theory, and signal and image processing are addressed within its pages.
We hope that the book will be interesting for pure and applied mathematicians in these areas, as well as for other researchers curious to discover more about fractals.
Amir Algom and Meng Wu: Large slices through self affine carpets.- Demi
Allen and Edouard Daviaud: A survey of recent extensions and generalisations
of the Mass Transference Principle.- Peter Arzt and Uta Freiberg: Spectral
Exponents of Gap Diffusions on Random Homogeneous Cantor-Sets.- Athanasios
Batakis, Nga Nguyen and Michel Zinsmeister: A new Model of City Growth and
its Application to a middle sized French City.- Wejdene Ben Nasr, Veronique
Billat, Stephane Jaffard,, Florent Palacin and Guillaume Sa?s: The weak
scaling multifractal spectrum: Mathematical setting and applications to
marathon runners physiological data.- Argyrios Christodoulou and Natalia
Jurga: Self-projective sets.- Herve Queffelec and Martine Queffelec: Old and
new results on the Furstenberg sets.- Michael Hochman: On the analytic
self-maps of Cantor sets in the line.- Xiong Jin: A Chung-Fuchs type theorem
for skew product dynamical systems.- Sabrina Kombrink and Lucas Schmidt:
Eigenvalue counting functions and parallel volumes for examples of fractal
sprays generated by the Koch snowflake.- Eugen Mihailescu: Exact dimensional
measures in deterministic and random systems.- Tuomas Sahlsten: Fourier
transforms and iterated function systems.- Nicolas de Saxce: A presentation
of the discretized sum-product in division algebras.- Xavier Tolsa:
Carlesons ??2 conjecture in higher dimensions and Faber-Krahn
inequalities.
Format: Paperback / softback, 340 pages, height x width: 235x155 mm, 1 Illustrations, color;
3 Illustrations, black and white; XIV, 340 p. 4 illus., 1 illus. in color.
Series: Universitext
Pub. Date: 10-Apr-2025
ISBN-13: 9783031817908
This textbook offers an accessible introduction to Functional Analysis, providing a solid foundation for students new to the field. It is designed to support learners with no prior background in the subject and serves as an effective guide for introductory courses, suitable for students in mathematics and other STEM disciplines.
The book provides a comprehensive introduction to the essential topics of Functional Analysis across the first seven chapters, with a particular emphasis on normed vector spaces, Banach spaces, and continuous linear operators. It examines the parallels and distinctions between Functional Analysis and Linear Algebra, highlighting the crucial role of continuity in infinite-dimensional spaces and its implications for complex mathematical problems.
Later chapters broaden the scope, including advanced topics such as topological vector spaces, techniques in Nonlinear Analysis, and key theorems in theory of Banach spaces. Exercises throughout the book reinforce understanding and allow readers to test their grasp of the material.
Designed for students in mathematics and other STEM disciplines, as well as researchers seeking a thorough introduction to Functional Analysis, this book takes a clear and accessible approach. Prerequisites include a strong foundation in analysis in the real line, linear algebra, and basic topology, with helpful references provided for additional consultation.
Contents.- Preface.- Normed Vector Spaces.- Continuous Linear
Operators.- Hahn-Banach Theorems.- Duality and Reflexive Spaces.- Hilbert
Spaces.- Weak Topologies.- Spectral Theories of Compact Self-Adjoint
Operators.- Topological Vector Spaces.- Introduction to Nonlinear Analysis.-
Elements of Banach Space Theory.- A Zorns Lemma.- B Concepts of General
Topology.- C Measure and Integration.- D Answers/hints for selected
exercises.- Bibliography.- Index.