الصفحة 10
الصفحة 10
Stochastic Calculus for Fractional Brownian Motion and Applications
Fractional Brownian motion (fBm) has been widely used to model a number of phenomena in diverse fields from biology to finance. This huge range of potential applications makes fBm an interesting object of study. fBm represents a natural one-parameter extension of classical Brownian motion therefore it is natural to ask if a stochastic calculus for fBm can be developed. This is not obvious, since fBm is neither a semimartingale (except when H = ½), nor a Markov process so the classical mathematical machineries for stochastic calculus are not available in the fBm case.
Stochastic and Integral Geometry
Stochastic geometry has in recent years experienced considerable progress, both in its applications to other sciences and engineering, and in its theoretical foundations and mathematical expansion. This book, by two eminent specialists of the subject, provides a solid mathematical treatment of the basic models of stochastic geometry -- random sets, point processes of geometric objects (particles, flats), and random mosaics. It develops, in a measure-theoretic setting, the integral geometry for the motion and the translation group, as needed for the investigation of these models under the usual invariance assumptions. A characteristic of the book is the interplay between stochastic and geometric arguments, leading to various major results. Its main theme, once the foundations have been laid, is the quantitative investigation of the basic models.
Statistics of Financial Markets : An Introduction
Statistics of Financial Markets offers a vivid yet concise introduction to the growing field of statistical applications in finance. The reader will learn the basic methods to evaluate option contracts, to analyse financial time series, to select portfolios and manage risks making realistic assumptions of the market behaviour. The focus is both on fundamentals of mathematical finance and financial time series analysis and on applications to given problems of financial markets, making the book the ideal basis for lectures, seminars and crash courses on the topic.
Statistical topics and stochastic models for dependent data with applications
A collective volume authored by leading scientists in the field of stochastic modelling, associated statistical topics and corresponding applications. The main classes of stochastic processes for dependent data investigated throughout this book are Markov, semi-Markov, autoregressive and piecewise deterministic Markov models. The material is divided into three parts corresponding to: (i) Markov and semi-Markov processes, (ii) autoregressive processes and (iii) techniques based on divergence measures and entropies.
Statistical Physics for Cosmic Structures
The physics of scale-invariant and complex systems is a novel interdisciplinary field. Its ideas allow us to look at natural phenomena in a radically new and original way, eventually leading to unifying concepts independent of the detailed structure of the systems. The objective is the study of complex, scale-invariant, and more general stochastic structures that appear both in space and time in a vast variety of natural phenomena, which exhibit new types of collective behaviors, and the fostering of their understanding. This book has been conceived as a methodological monograph in which the main methods of modern statistical physics for cosmological structures and density fields (galaxies, Cosmic Microwave Background Radiation, etc.) are presented in detail. The main purpose is to present clearly, to a workable level, these methods, with a certain mathematical accuracy, providing also some paradigmatic examples of applications.
Statistical Monitoring of Clinical Trials : Fundamentals for Investigators
Statistical Monitoring of Clinical Trials: Fundamentals for Investigators introduces the investigator and statistician to monitoring procedures in clinical research. Clearly presenting the necessary background with limited use of mathematics, this book increases the knowledge, experience, and intuition of investigations in the use of these important procedures now required by the many clinical research efforts.
Statistical Monitoring of Clinical Trials : A Unified Approach
Shows that the joint distribution of the test statistics at different analysis times is asymptotically multivariate normal with the correlation structure of Brownian motion (``the B-value") irrespective of the test statistic. The so-called B-value approach to monitoring allows us to use, for different types of trials, the same boundaries and the same simple formula for computing conditional power.
Statistical Models and Methods for Biomedical and Technical Systems
An outgrowth of the "International Conference on Statistical Models for Biomedical and Technical Systems," this book is comprised of contributions from renowned experts, demonstrating the significance of current research on theory, methods, and applications of the field. The contributions, which deal with the mathematical aspects of survival analysis and reliability as well as other topics. The book will be useful to a broad interdisciplinary readership of researchers and practitioners in applied probability and statistics, industrial statistics, biomedicine, biostatistics, and engineering. Practitioners and researchers in academia will gain insight and new ideas for exploring this fertile area of research.
Statistical Implicative Analysis : Theory and Applications
This volume collects significant research contributions of several rather distinct disciplines that benefit from SIA. Contributions range from psychological and pedagogical research, bioinformatics, knowledge management, and data mining.
Statistical Decision Theory : Estimation, Testing, and Selection
This monograph is written for advanced graduate students, Ph.D. students, and researchers in mathematical statistics and decision theory. All major topics are introduced on a fairly elementary level and then developed gradually to higher levels. The book is self-contained as it provides full proofs, worked-out examples, and problems. It can be used as a basis for graduate courses, seminars, Ph.D. programs, self-studies, and as a reference book.
Statistical analysis of molecular and genomic evolution
Proposes a new framework of knowledge for the field of evolutionary genomics. Written at the simplest mathematical level while offering a clear explanation of complex statistical models and principles. Includes web-based computer practical exercises and online appendices to clarify the theory and facilitate student tuition
Static Analysis ; 15th International Symposium, SAS 2008, Valencia, Spain, July 16-18, 2008. Proceedings
The book addresses all aspects of static analysis including abstract domains, abstract interpretation, abstract testing, compiler optimizations, control flow analysis, data flow analysis, model checking, program specialization, security analysis, theoretical analysis frameworks, type based analysis, and verification systems.
Stable Approximate Evaluation of Unbounded Operators
Spectral theory of bounded linear operators teams up with von Neumann’s theory of unbounded operators in this monograph to provide a general framework for the study of stable methods for the evaluation of unbounded operators. An introductory chapter provides numerous illustrations of unbounded linear operators that arise in various inverse problems of mathematical physics. Before the general theory of stabilization methods is developed, an extensive exposition of the necessary background material from the theory of operators on Hilbert space is provided. Several specific stabilization methods are studied in detail, with particular attention to the Tikhonov-Morozov method and its iterated version.
Stabilization, Optimal and Robust Control : Theory and Applications in Biological and Physical Sciences
Systems governed by nonlinear partial differential equations (PDEs) arise in many spheres of study. The stabilization and control of such systems, which are the focus of this book, are based around game theory. The robust control methods proposed here have the twin aims of compensating for system disturbances in such a way that a cost function achieves its minimum for the worst disturbances and providing the best control for stabilizing fluctuations with a limited control effort.Mathematical foundations essential for the required analysis are provided so that the book remains accessible to the non-control-specialist. Following chapters giving a general view of convex analysis and optimization and robust and optimal control, problems arising in fluid-mechanical, biological and materials-scientific systems are laid out in detail; specifically
Stability of Nonautonomous Differential Equations
Main theme of this volume is the stability of nonautonomous differential equations, with emphasis on the Lyapunov stability of solutions, the existence and smoothness of invariant manifolds, the construction and regularity of topological conjugacies, the study of center manifolds, as well as their reversibility and equivariance properties. Most results are obtained in the infinite-dimensional setting of Banach spaces. Furthermore, the linear variational equations are always assumed to possess a nonuniform exponential behavior, given either by the existence of a nonuniform exponential contraction or a nonuniform exponential dichotomy. The presentation is self-contained and has unified character. The volume contributes towards a rigorous mathematical foundation of the theory in the infinite-dimension setting, and may lead to further developments in the field. The exposition is directed to researchers as well as graduate students interested in differential equations and dynamical systems, particularly in stability theory.
Stability and Wave Motion in Porous Media
Describes several tractable theories for fluid flow in porous media while the important mathematical questions about structural stability and spatial decay are addressed. Thermal convection and stability of other flows in porous media are covered and a chapter is devoted to the problem of stability of flow in a fluid overlying a porous layer. Nonlinear wave motion in porous media is analysed, and waves in an elastic body with voids are investigated. Acoustic waves in porous media are also analysed in some detail.
Stability and Convergence of Mechanical Systems with Unilateral Constraints
Stability of motion is a central theme in the dynamics of mechanical systems. While the stability theory for systems with bilateral constraints is a well-established field, this monograph represents a systematic study of mechanical systems with unilateral constraints, such as unilateral contact, impact and friction. Such unilateral constraints give rise to non-smooth dynamical models for which stability theory is developed in this work.The book starts with the treatise of the mathematical background on non-smooth analysis, measure and integration theory and an introduction to the field of non-smooth dynamical systems. The unilateral constraints are modelled in the framework of set-valued force laws developed in the field of non-smooth mechanics.
Square-Wave Voltammetry : Theory and Application
Square-wave voltammetry is a technique readily available to every researcher, scientist, engineer and practitioner applying modern electrochemical measurement systems. It is of beneficial use in analytical applications and in fundamental studies of electrode mechanisms. But the optimised exploitation of this technique is only possible for those with a detailed knowledge of signal generation and of the thermodynamics and kinetics involved. This volume, written by three distiguished experts, systematically delivers the complete and in-depth information that enables both researchers and users of square-wave voltammetry to apply this technique effectively. Square-Wave Voltammetry also offers an appendix on mathematical modeling and a chapter on the most important electrode mechanisms which briefly reviews the underlying theory and numerical formulae intrinsic for simulating experiments with popular software tools
Special Functions for Applied Scientists
Special Functions for Applied Scientists provides the required mathematical tools for researchers active in the physical sciences. The book presents a full suit of elementary functions for scholars at the PhD level and covers a wide-array of topics and begins by introducing elementary classical special functions. From there, differential equations and some applications into statistical distribution theory are examined. The fractional calculus chapter covers fractional integrals and fractional derivatives as well as their applications to reaction-diffusion problems in physics, input-output analysis, Mittag-Leffler stochastic processes and related topics.
SPDE in Hydrodynamic : Recent Progress and Prospects : Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy August 29–September 3, 2005
Of the three lecture courses making up the CIME summer school on Fluid Dynamics at Cetraro in 2005 reflected in this volume, the first, due to Sergio Albeverio describes deterministic and stochastic models of hydrodynamics. In the second course, Franco Flandoli starts from 3D Navier-Stokes equations and ends with turbulence. Finally,Yakov Sinai, in the 3rd course, describes some rigorous mathematical results for multidimensional Navier-Stokes systems and some recent results on the one-dimensional Burgers equation with random forcing.
