Series: Springer Monographs in Mathematics
Originally published as volume 508 in the series: Mathematics and Its Applications
2015, XIV, 666 p. With XII, 638.
Hardcover
ISBN 978-3-319-12171-0
Due: January 14, 2015
Provides a rigorous introduction to stochastic analysis and inference theory
Enriches understanding of nontrivial statistical inference problems on stochastic processes
Gives inside in Kalman filter analysis and recent discussions on Ridge regressions and related theory
This is the revised and enlarged 2nd edition of the authorsf original text, which was intended to be a modest complement to Grenander's fundamental memoir on stochastic processes and related inference theory. The present volume gives a substantial account of regression analysis, both for stochastic processes and measures, and includes recent material on Ridge regression with some unexpected applications, for example in econometrics.
The first three chapters can be used for a quarter or semester graduate course on inference on stochastic processes. The remaining chapters provide more advanced material on stochastic analysis suitable for graduate seminars and discussions, leading to dissertation or research work. In general, the book will be of interest to researchers in probability theory, mathematical statistics and electrical and information theory.
1.Introduction and Preliminaries.- 2.Some Principles of Hypothesis Testing.- 3.Parameter Estimation and Asymptotics.- 4.Inferences for Classes of Processes.- 5.Likelihood Ratios for Processes.- 6.Sampling Methods for Processes.- 7.More on Stochastic Inference.- 8.Prediction and Filtering of Processes.- 9.Nonparametric Estimation for Processes.- Bibliography.- Index.
2015, XVIII, 216 p. 18 illus., 10 illus. in color.
Softcover
ISBN 978-3-658-07617-7
After revising known representations of the group of Euclidean displacements Daniel Klawitter gives a comprehensive introduction into Clifford algebras. The Clifford algebra calculus is used to construct new models that allow descriptions of the group of projective transformations and inversions with respect to hyperquadrics. Afterwards, chain geometries over Clifford algebras and their subchain geometries are examined. The author applies this theory and the developed methods to the homogeneous Clifford algebra model corresponding to Euclidean geometry. Moreover, kinematic mappings for special Cayley-Klein geometries are developed. These mappings allow a description of existing kinematic mappings in a unifying framework.
Models and representations of classical groups
Clifford algebras, chain geometries over Clifford algebras
Kinematic mappings for Pin and Spin groups
Cayley-Klein geometries
Daniel Klawitter is a scientific assistant at the Institute of Geometry at the Technical University of Dresden, Germany.
Series: Springer Proceedings in Mathematics & Statistics, Vol. 113
2015, XVII, 337 p. 12 illus.
Hardcover
ISBN 978-3-319-12144-4
Due: February 14, 2015
Includes cutting edge results in semigroup theory and up-to-date applications of semigroups
Treats stochastic control in biological problems
Bridges gaps between theory and applications
Many results, both from semigroup theory itself and from the applied sciences, are phrased in discipline-specific languages and hence are hardly known to a broader community. This volume contains a selection of lectures presented at a conference that was organised as a forum for all mathematicians using semigroup theory to learn what is happening outside their own field of research. The collection will help to establish a number of new links between various sub-disciplines of semigroup theory, stochastic processes, differential equations and the applied fields.
The theory of semigroups of operators is a well-developed branch of functional analysis. Its foundations were laid at the beginning of the 20th century, while the fundamental generation theorem of Hille and Yosida dates back to the forties. The theory was, from the very beginning, designed as a universal language for partial differential equations and stochastic processes, but at the same time it started to live as an independent branch of operator theory. Nowadays, it still has the same distinctive flavour: it develops rapidly by posing new einternalf questions and, in answering them, discovering new methods that can be used in applications. On the other hand, it is influenced by questions from PDEs and stochastic processes as well as from applied sciences such as mathematical biology and optimal control, and thus it continually gathers a new momentum. Researchers and postgraduate students working in operator theory, partial differential equations, probability and stochastic processes, analytical methods in biology and other natural sciences, optimization and optimal control will find this volume useful.
Jerome A. Goldstein, Rainer Nagel: The Evolution of Operator Semigroups.- Krzysztof Bogdan, Sebastian Sydor: On nonlocal perturbations of integral kernels.- Jan KisyLnski: Convolution operators as generators of one-parameter semigroups.- Jan KisyLnski: One-parameter semigroups in the algebra of slowly increasing functions.- Delio Mugnolo: Some remarks on the Krein?von Neumann extension of different Laplacians.- Mustapha Mokhtar-Kharroubi: On strong convergence to ergodic projection for perturbed substochastic semigroups.- Lassi Paunonen: On Robustness of Strongly Stable Semigroups with Spectrum on iR.- Irena Lasiecka, Roberto Triggiani: Uniform Stabilization with Arbitrary Decay Rates of the Oseen Equation by Finite-Dimensional Tangential Localized Interior and Boundary Controls.- H. Emamirad, G. R. Goldstein, J. A. Goldstein, P. Rogeon: The null volatility limit of the chaotic Black-Scholes equation.- V. I. Gerasimenko, Yu. Yu. Fedchun: On Semigroups of Large Particle Systems and their Scaling Asymptotic Behavior.- Alevtina V. Keller, Alexander L. Shestakov, Georgy A. Sviridyuk, Yurii V. Khudyakov: The Numerical Algorithms for the Measurement of the Deterministic and Stochastic Signals.- Yuri Kozitsky: Dynamics of spatial logistic model: finite systems.- Natalia A. Manakova, Georgy A. Sviridyuk: An Optimal Control of the Solutions of the Initial-Final Problem for Linear Sobolev Type Equations with Strongly Relatively p-Radial Operator.- Irina V. Melnikova, Valentina S. Parfenenkova: Two approaches to infinite dimensional extension of Feynman?Kac theorem.- Ryszard Rudnicki, Marta Tyran-KamiLnska: Piecewise deterministic Markov processes in biological models.- Minzilia A. Sagadeeva, Georgy A. Sviridyuk: The Nonautonomous Linear Oskolkov Model on a Geometrical Graph: the Stability of Solutions and the Optimal Control Problem.- S. A. Stepin: Complex Potentials: Bound States, Quantum Dynamics and Wave Operators.- Andrzej Tomski: The Dynamics of Enzyme Inhibition Controlled by Piece-wise Deterministic Markov Process.- Sophiya A. Zagrebina, Ekaterina A. Soldatova, Georgy A. Sviridyuk: The Stochastic Linear Oskolkov Model of the Oil Transportation by the Pipeline,- Alyona A. Zamyshlyaeva, Georgy A. Sviridyuk: The Linearized Benney ? Luke Mathematical Model with Additive White Noise.
Series: Applied Mathematical Sciences, Vol. 191
2014, XIV, 950 p. 189 illus., 47 illus. in color.
Hardcover
ISBN 978-3-319-12315-8
Due: January 14, 2015
Interdisciplinary approach to multiple time scale dynamics
Includes many exercises and direct transition to research-level questions
Links different mathematical areas and different viewpoints
Highly illustrated
This book provides an introduction to dynamical systems with multiple time scales. The approach it takes is to provide an overview of key areas, particularly topics that are less available in the introductory form. The broad range of topics included makes it accessible for students and researchers new to the field to gain a quick and thorough overview.
The first of its kind, this book merges a wide variety of different mathematical techniques into a more unified framework. The book is highly illustrated with many examples and exercises and an extensive bibliography. The target audience of this book are senior undergraduates, graduate students as well as researchers interested in using the multiple time scale dynamics theory in nonlinear science, either from a theoretical or a mathematical modeling perspective.
Introduction.- General Fenichel Theory.- Geometric Singular Perturbation Theory.- Normal Forms.- Direct Asymptotic Methods.- Tracking Invariant Manifolds.- The Blow-Up Method.- Singularities and Canards.- Advanced Asymptotic Methods.- Numerical Methods.- Computing Manifolds.- Scaling and Delay.- Oscillations.- Chaos in Fast-Slow Systems.- Stochastic Systems.- Topological Methods.- Spatial Dynamics.- Infinite Dimensions.- Other Topics.- Applications.
Series: Applied Mathematical Sciences, Vol. 192
2014, XXXI, 862 p. 202 illus., 100 illus. in color.
Hardcover
ISBN 978-3-319-12747-7
Due: January 14, 2015
Provides a unique interdisciplinary treatment of the nonlinear Schrodinger equation, combining rigorous analysis, informal analysis, numerical methods and physics
Presents all the necessary physical background, and assumes only that the reader has taken an introductory class in partial differential equations
Carefully explains the theory, application and background of the nonlinear Schrodinger equation in nonlinear optics
Covers the theory of NLS collapse from the early 1960s and up to the present
This book is an interdisciplinary introduction to optical collapse of laser beams, which is modelled by singular (blow-up) solutions of the nonlinear Schrodinger equation. With great care and detail, it develops the subject including the mathematical and physical background and the history of the subject. It combines rigorous analysis, asymptotic analysis, informal arguments, numerical simulations, physical modelling, and physical experiments. It repeatedly emphasizes the relations between these approaches, and the intuition behind the results.
The Nonlinear Schrodinger Equation will be useful to graduate students and researchers in applied mathematics who are interested in singular solutions of partial differential equations, nonlinear optics and nonlinear waves, and to graduate students and researchers in physics and engineering who are interested in nonlinear optics and Bose-Einstein condensates. It can be used for courses on partial differential equations, nonlinear waves, and nonlinear optics.
Gadi Fibich is a Professor of Applied Mathematics at Tel Aviv University.
Derivation of the NLS.- Linear propagation.- Early self-focusing research.- NLS models.- Existence of NLS solutions.- Solitary waves.- Variance identity.- Symmetries and the lens transformation.- Stability of solitary waves.- The explicit critical singular peak-type solution.- The explicit critical singular ring-type solution.- The explicit supercritical singular peak-type solution.- Blowup rate, blowup profile, and power concentration.- The peak-type blowup profile.- Vortex solutions.- NLS on a bounded domain.- Derivation of reduced equations.- Loglog law and adiabatic collapse.- Singular H1 ring-type solutions.- Singular H1 vortex solutions.- Singular H1 peak-type solutions.- Singular standing-ring solutions.- Singular shrinking-ring solutions.- Critical and threshold powers for collapse.- Multiple filamentation.- Nonlinear Geometrical Optics (NGO) method.- Location of singularity.- Computation of solitary waves.- Numerical methods for the NLS.- Effects of spatial discretization.- Modulation theory.- Cubic-quintic and saturated nonlinearities.- Linear and nonlinear damping.- Nonparaxiality and backscattering (nonlinear Helmholtz equation).- Ultrashort pulses.- Normal and anomalous dispersion.- NGO method for ultrashort pulses with anomalous dispersion.- Continuations beyond the singularity.- Loss of phase and chaotic interactions.