Statistical Properties Of Discrete Deterministic Systems
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| Author | : Jiu Ding |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 248 |
| Release | : 2010-06-28 |
| Genre | : Mathematics |
| ISBN | : 3540853677 |
Part of Tsinghua University Texts, "Statistical Properties of Deterministic Systems" discusses the fundamental theory and computational methods of the statistical properties of deterministic discrete dynamical systems. After introducing some basic results from ergodic theory, two problems related to the dynamical system are studied: first the existence of absolute continuous invariant measures, and then their computation. They correspond to the functional analysis and numerical analysis of the Frobenius-Perron operator associated with the dynamical system. The book can be used as a text for graduate students in applied mathematics and in computational mathematics; it can also serve as a reference book for researchers in the physical sciences, life sciences, and engineering. Dr. Jiu Ding is a professor at the Department of Mathematics of the University of Southern Mississippi; Dr. Aihui Zhou is a professor at the Academy of Mathematics and Systems Science of the Chinese Academy of Sciences.
| Author | : Andrzej Lasota |
| Publisher | : Cambridge University Press |
| Total Pages | : 376 |
| Release | : 2008-11-27 |
| Genre | : Mathematics |
| ISBN | : 9780521090964 |
This book shows how densities arise in simple deterministic systems. There has been explosive growth in interest in physical, biological and economic systems that can be profitably studied using densities. Due to the inaccessibility of the mathematical literature there has been little diffusion of the applicable mathematics into the study of these 'chaotic' systems. This book will help to bridge that gap. The authors give a unified treatment of a variety of mathematical systems generating densities, ranging from one-dimensional discrete time transformations through continuous time systems described by integro-partial differential equations. They have drawn examples from many scientific fields to illustrate the utility of the techniques presented. The book assumes a knowledge of advanced calculus and differential equations, but basic concepts from measure theory, ergodic theory, the geometry of manifolds, partial differential equations, probability theory and Markov processes, and stochastic integrals and differential equations are introduced as needed.
| Author | : Gangaram S Ladde |
| Publisher | : World Scientific |
| Total Pages | : 355 |
| Release | : 2024-04-22 |
| Genre | : Mathematics |
| ISBN | : 981128749X |
Continuous state dynamic models can be reformulated into discrete state processes. This process generates numerical schemes that lead theoretical iterative schemes. This type of method of stochastic modelling generates three basic problems. First, the fundamental properties of solution, namely, existence, uniqueness, measurability, continuous dependence on system parameters depend on mode of convergence. Second, the basic probabilistic and statistical properties, namely, the behavior of mean, variance, moments of solutions are described as qualitative/quantitative properties of solution process. We observe that the nature of probability distribution or density functions possess the qualitative/quantitative properties of iterative prosses as a special case. Finally, deterministic versus stochastic modelling of dynamic processes is to what extent the stochastic mathematical model differs from the corresponding deterministic model in the absence of random disturbances or fluctuations and uncertainties.Most literature in this subject was developed in the 1950s, and focused on the theory of systems of continuous and discrete-time deterministic; however, continuous-time and its approximation schemes of stochastic differential equations faced the solutions outlined above and made slow progress in developing problems. This monograph addresses these problems by presenting an account of stochastic versus deterministic issues in discrete state dynamic systems in a systematic and unified way.
| Author | : Kenneth Train |
| Publisher | : Cambridge University Press |
| Total Pages | : 399 |
| Release | : 2009-07-06 |
| Genre | : Business & Economics |
| ISBN | : 0521766559 |
This book describes the new generation of discrete choice methods, focusing on the many advances that are made possible by simulation. Researchers use these statistical methods to examine the choices that consumers, households, firms, and other agents make. Each of the major models is covered: logit, generalized extreme value, or GEV (including nested and cross-nested logits), probit, and mixed logit, plus a variety of specifications that build on these basics. Simulation-assisted estimation procedures are investigated and compared, including maximum stimulated likelihood, method of simulated moments, and method of simulated scores. Procedures for drawing from densities are described, including variance reduction techniques such as anithetics and Halton draws. Recent advances in Bayesian procedures are explored, including the use of the Metropolis-Hastings algorithm and its variant Gibbs sampling. The second edition adds chapters on endogeneity and expectation-maximization (EM) algorithms. No other book incorporates all these fields, which have arisen in the past 25 years. The procedures are applicable in many fields, including energy, transportation, environmental studies, health, labor, and marketing.
| Author | : W. Q. Zhu |
| Publisher | : CRC Press |
| Total Pages | : 626 |
| Release | : 2003-05-13 |
| Genre | : Technology & Engineering |
| ISBN | : 0203492951 |
Collection of technical papers presented at the 5th International Conference on Stochastic Structural Dynamics (SSD03) in Hangzhou, China during May 26-28, 2003. Topics include direct transfer substructure method for random response analysis, generation of bounded stochastic processes, and sample path behavior of Gaussian processes.
| Author | : Jose Miguel Arias |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 356 |
| Release | : 2004-11-23 |
| Genre | : Science |
| ISBN | : 9783540225126 |
Powerful new techniques, including heavy ion and exotic beams, are pushing the frontiers of nuclear physics and opening up a wealth of new fields of research. After introductory chapters on theoretical and experimental aspects of nuclear collisions and beams, ``Exotic Nuclear Physics'' offers articles by experienced lecturers on forefront topics in nuclear physics, such as the conquest of the neutron and the proton drip-lines, nuclear astrophysics, the equation of state of hypernuclear matter, nuclear supersymmetry and chaotic motion in nuclei. This volume continues the successful tradition of published lecture notes from the Hispalensis International Summer School. It will benefit graduate students and lecturers in search of advanced material for self-study and courses as will as researchers in search of a modern and comprehensive source of reference.
| Author | : |
| Publisher | : |
| Total Pages | : 854 |
| Release | : |
| Genre | : Military research |
| ISBN | : |
| Author | : Akira Namatame |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 345 |
| Release | : 2006-03-09 |
| Genre | : Business & Economics |
| ISBN | : 3540287272 |
Understanding the mechanism of a socio-economic system requires more than an understanding of the individuals that comprise the system. It also requires understanding how individuals interact with each other, and how the agg- gated outcome can be more than the sum of individual behaviors. This book contains the papers fostering the formation of an active multi-disciplinary community on socio-economic systems with the exciting new ?elds of age- based modeling and econophysics. We especially intend to increase the awareness of researchers in many ?elds with sharing the common view many economic and social activities as collectives of a large-scale heterogeneous and interacting agents. Economists seek to understand not only how individuals behave but also how the interaction of many individuals leads to complex outcomes. Age- based modeling is a method for studying socio-economic systems exhibiting the following two properties: (1) the system is composed of interacting agents, and (2) the system exhibits emergent properties, that is, properties arising from the interactions of the agents that cannot be deduced simply by agg- gating the properties of the system’s components. When the interaction of the agents is contingent on past experience, and especially when the agents continually adapt to that experience, mathematical analysis is typically very limited in its ability to derive the outcome.
| Author | : Arun K. Tangirala |
| Publisher | : CRC Press |
| Total Pages | : 881 |
| Release | : 2018-10-08 |
| Genre | : Technology & Engineering |
| ISBN | : 143989602X |
Master Techniques and Successfully Build Models Using a Single Resource Vital to all data-driven or measurement-based process operations, system identification is an interface that is based on observational science, and centers on developing mathematical models from observed data. Principles of System Identification: Theory and Practice is an introductory-level book that presents the basic foundations and underlying methods relevant to system identification. The overall scope of the book focuses on system identification with an emphasis on practice, and concentrates most specifically on discrete-time linear system identification. Useful for Both Theory and Practice The book presents the foundational pillars of identification, namely, the theory of discrete-time LTI systems, the basics of signal processing, the theory of random processes, and estimation theory. It explains the core theoretical concepts of building (linear) dynamic models from experimental data, as well as the experimental and practical aspects of identification. The author offers glimpses of modern developments in this area, and provides numerical and simulation-based examples, case studies, end-of-chapter problems, and other ample references to code for illustration and training. Comprising 26 chapters, and ideal for coursework and self-study, this extensive text: Provides the essential concepts of identification Lays down the foundations of mathematical descriptions of systems, random processes, and estimation in the context of identification Discusses the theory pertaining to non-parametric and parametric models for deterministic-plus-stochastic LTI systems in detail Demonstrates the concepts and methods of identification on different case-studies Presents a gradual development of state-space identification and grey-box modeling Offers an overview of advanced topics of identification namely the linear time-varying (LTV), non-linear, and closed-loop identification Discusses a multivariable approach to identification using the iterative principal component analysis Embeds MATLAB® codes for illustrated examples in the text at the respective points Principles of System Identification: Theory and Practice presents a formal base in LTI deterministic and stochastic systems modeling and estimation theory; it is a one-stop reference for introductory to moderately advanced courses on system identification, as well as introductory courses on stochastic signal processing or time-series analysis.The MATLAB scripts and SIMULINK models used as examples and case studies in the book are also available on the author's website: http://arunkt.wix.com/homepage#!textbook/c397
| Author | : University of Michigan |
| Publisher | : UM Libraries |
| Total Pages | : 108 |
| Release | : 1974 |
| Genre | : Education, Higher |
| ISBN | : |
Each number is the catalogue of a specific school or college of the University.
