Offers mathematically oriented statisticians tools for studying non-linear timeseries
Discusses moment based techniques
Richly illustrated with examples and simulations
Provides material for mathematicians entering the field of non-linear time series
This book presents essential tools for modelling non-linear time series. The first part of the
book describes the main standard tools of probability and statistics that directly apply to the
time series context to obtain a wide range of modelling possibilities. Functional estimation and
bootstrap are discussed, and stationarity is reviewed. The second part describes a number of
tools from Gaussian chaos and proposesa tour of linear time series models.It goes on to
address nonlinearity from polynomial or chaotic models for which explicit expansions are
available,then turns to Markov and non-Markov linear models and discusses Bernoulli shifts
time series models.Finally, the volume focuses on the limit theory, starting with the ergodic
theorem, which is seen as the first step for statistics of time series. It defines the distributional
range to obtain generic tools for limit theory under long or short-range dependences (LRD
/SRD) and explains examples of LRD behaviours. More general techniques (central limit
theorems) are described under SRD; mixing and weak dependence are also reviewed. In
closing, it describes moment techniques together with their relations to cumulant sums as well
as an application to kernel type estimation.The appendix reviews basic probability theory facts
and discusses useful laws stemming from the Gaussian laws as well as the basic principles of
probability, and is completed by R-scripts used for the figures.Richly illustrated with examples
and simulations, the book is recommended for advanced master courses for mathematicians
just entering the field of time series, and statisticians who want more mathematical insights
into the background of non-linear time series.
ISBN 978-3-319-76937-0
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Includes the first complete treatment of geometric motivic integration in a monograph
Covers the construction of arc schemes and Greenberg schemes
Provides a complete discussion of questions concerning the Grothendieck ring
of varieties and its algebraic structure
This monograph focuses on the geometric theory of motivic integration, which takes its values
in the Grothendieck ring of varieties. This theory is rooted in a groundbreaking idea of
Kontsevich and was further developed by Denef & Loeser and Sebag. It is presented in the
context of formal schemes over a discrete valuation ring, without any restriction on the residue
characteristic. The text first discusses the main features of the Grothendieck ring of varieties,
arc schemes, and Greenberg schemes. It then moves on to motivic integration and its
applications to birational geometry and non-Archimedean geometry. Also included in the work
is a prologue on p-adic analytic manifolds, which served as a model for motivic integration.
With its extensive discussion of preliminaries and applications, this book is an ideal resource for
graduate students of algebraic geometry and researchers of motivic integration. It will also
serve as a motivation for more recent and sophisticated theories that have been developed since.
ISBN 978-1-4939-7885-4
274pp Feb 2019
ISBN: 978-981-3235-42-7 (hardcover)
From Tzuong-Tsieng Moh, a long-time expert in algebra, comes a new book for students to better understand linear algebra. Writing from an experienced standpoint, Moh touches on the many facets surrounding linear algebra, including but not limited to, echelon forms, matrix algebra, linear transformations, determinants, dual space, inner products, the Gram?Schmidt Theorem, Hilbert space, and more. It is ideal for both newcomers and seasoned readers who want to attain a deeper understanding on both the basics and advanced topics of linear algebra and its vast applications. The wide range of topics combined with the depth of each discussion make it essential to be on the shelf of every mathematical beginner and enthusiast.
Echelon Form, Matrix Algebra, Hamming Code
Linear Transformation, Dot Product, Geometry
The Fundamental Theorem of Matrix, Kirchhoff's Law
Determinant, Dimension Theory of General Vector Spaces
Ring, Module, Free Module
Finitely Generated Module over P.I.D.
Smith Normal Form, Application to Coding Theory
Rational Form, Characteristic Polynomial
Torsion Decomposition, Elementary Decomposition
Jordan Canonical Form, Differential Equation
Eigenvalue, Eigenvector, Cayley?Hamilton Theorem
Simultaneously Diagonalizable Matrices
Cauchy?Binet Formula, m-dimensional Volume in Rn
Tensor Product, Exterior Product, Differential Geometry
Dual Space, Application to Physics
Chain Complex, Co-chain Complex, Koszul Complex
Projective, Injective, Flat Modules, Resolutions, Ext, Tor
Inner Product, Gram?Schmidt Theorem
Hook's Law, Least Squares Approximation
Hilbert Space, Perpendicular Complement
Adjoint, Self-Adjoint Operator, Heisenberg's Uncertainty Principle
Minimal Problem, Positive-Definite Matrix
Multiple Variable Function, Unitary Operator, Spectrum Theorem
Singular Value Decomposition, Applications
Bilinear Form, Sylvester's Law of Inertia
Groups Preserving Bilinear Form, Special Relativity
Numerical Model, Finite Element Method
Solve a System of Linear Equations Numerically
Power Method, Perron?Frobenius Theorem, Google Search
QR Method, Solve a Polynomial Numerically
Readership: Graduate students and researchers interested in the basic and advanced topics of linear algebra and its applications.