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Author: M. H. A. Davis Publisher: Springer ISBN: Category : Juvenile Nonfiction Languages : en Pages : 416
Book Description
This book aims to provide a unified treatment of input/output modelling and of control for discrete-time dynamical systems subject to random disturbances. The results presented are of wide applica bility in control engineering, operations research, econometric modelling and many other areas. There are two distinct approaches to mathematical modelling of physical systems: a direct analysis of the physical mechanisms that comprise the process, or a 'black box' approach based on analysis of input/output data. The second approach is adopted here, although of course the properties ofthe models we study, which within the limits of linearity are very general, are also relevant to the behaviour of systems represented by such models, however they are arrived at. The type of system we are interested in is a discrete-time or sampled-data system where the relation between input and output is (at least approximately) linear and where additive random dis turbances are also present, so that the behaviour of the system must be investigated by statistical methods. After a preliminary chapter summarizing elements of probability and linear system theory, we introduce in Chapter 2 some general linear stochastic models, both in input/output and state-space form. Chapter 3 concerns filtering theory: estimation of the state of a dynamical system from noisy observations. As well as being an important topic in its own right, filtering theory provides the link, via the so-called innovations representation, between input/output models (as identified by data analysis) and state-space models, as required for much contemporary control theory.
Author: M. H. A. Davis Publisher: Springer ISBN: Category : Juvenile Nonfiction Languages : en Pages : 416
Book Description
This book aims to provide a unified treatment of input/output modelling and of control for discrete-time dynamical systems subject to random disturbances. The results presented are of wide applica bility in control engineering, operations research, econometric modelling and many other areas. There are two distinct approaches to mathematical modelling of physical systems: a direct analysis of the physical mechanisms that comprise the process, or a 'black box' approach based on analysis of input/output data. The second approach is adopted here, although of course the properties ofthe models we study, which within the limits of linearity are very general, are also relevant to the behaviour of systems represented by such models, however they are arrived at. The type of system we are interested in is a discrete-time or sampled-data system where the relation between input and output is (at least approximately) linear and where additive random dis turbances are also present, so that the behaviour of the system must be investigated by statistical methods. After a preliminary chapter summarizing elements of probability and linear system theory, we introduce in Chapter 2 some general linear stochastic models, both in input/output and state-space form. Chapter 3 concerns filtering theory: estimation of the state of a dynamical system from noisy observations. As well as being an important topic in its own right, filtering theory provides the link, via the so-called innovations representation, between input/output models (as identified by data analysis) and state-space models, as required for much contemporary control theory.
Author: Charles S. Tapiero Publisher: Springer Science & Business Media ISBN: 1461558239 Category : Business & Economics Languages : en Pages : 352
Book Description
Applied Stochastic Models and Control for Finance and Insurance presents at an introductory level some essential stochastic models applied in economics, finance and insurance. Markov chains, random walks, stochastic differential equations and other stochastic processes are used throughout the book and systematically applied to economic and financial applications. In addition, a dynamic programming framework is used to deal with some basic optimization problems. The book begins by introducing problems of economics, finance and insurance which involve time, uncertainty and risk. A number of cases are treated in detail, spanning risk management, volatility, memory, the time structure of preferences, interest rates and yields, etc. The second and third chapters provide an introduction to stochastic models and their application. Stochastic differential equations and stochastic calculus are presented in an intuitive manner, and numerous applications and exercises are used to facilitate their understanding and their use in Chapter 3. A number of other processes which are increasingly used in finance and insurance are introduced in Chapter 4. In the fifth chapter, ARCH and GARCH models are presented and their application to modeling volatility is emphasized. An outline of decision-making procedures is presented in Chapter 6. Furthermore, we also introduce the essentials of stochastic dynamic programming and control, and provide first steps for the student who seeks to apply these techniques. Finally, in Chapter 7, numerical techniques and approximations to stochastic processes are examined. This book can be used in business, economics, financial engineering and decision sciences schools for second year Master's students, as well as in a number of courses widely given in departments of statistics, systems and decision sciences.
Author: Andreas Diekmann Publisher: Academic Press ISBN: 1483266567 Category : Social Science Languages : en Pages : 352
Book Description
Stochastic Modelling of Social Processes provides information pertinent to the development in the field of stochastic modeling and its applications in the social sciences. This book demonstrates that stochastic models can fulfill the goals of explanation and prediction. Organized into nine chapters, this book begins with an overview of stochastic models that fulfill normative, predictive, and structural–analytic roles with the aid of the theory of probability. This text then examines the study of labor market structures using analysis of job and career mobility, which is one of the approaches taken by sociologists in research on the labor market. Other chapters consider the characteristic trends and patterns from data on divorces. This book discusses as well the two approaches of stochastic modeling of social processes, namely competing risk models and semi-Markov processes. The final chapter deals with the practical application of regression models of survival data. This book is a valuable resource for social scientists and statisticians.
Author: George Yin Publisher: Springer ISBN: 3030254984 Category : Mathematics Languages : en Pages : 599
Book Description
This volume collects papers, based on invited talks given at the IMA workshop in Modeling, Stochastic Control, Optimization, and Related Applications, held at the Institute for Mathematics and Its Applications, University of Minnesota, during May and June, 2018. There were four week-long workshops during the conference. They are (1) stochastic control, computation methods, and applications, (2) queueing theory and networked systems, (3) ecological and biological applications, and (4) finance and economics applications. For broader impacts, researchers from different fields covering both theoretically oriented and application intensive areas were invited to participate in the conference. It brought together researchers from multi-disciplinary communities in applied mathematics, applied probability, engineering, biology, ecology, and networked science, to review, and substantially update most recent progress. As an archive, this volume presents some of the highlights of the workshops, and collect papers covering a broad range of topics.
Author: Mark Davis Publisher: Springer Science & Business Media ISBN: 940094828X Category : Science Languages : en Pages : 405
Book Description
This book aims to provide a unified treatment of input/output modelling and of control for discrete-time dynamical systems subject to random disturbances. The results presented are of wide applica bility in control engineering, operations research, econometric modelling and many other areas. There are two distinct approaches to mathematical modelling of physical systems: a direct analysis of the physical mechanisms that comprise the process, or a 'black box' approach based on analysis of input/output data. The second approach is adopted here, although of course the properties ofthe models we study, which within the limits of linearity are very general, are also relevant to the behaviour of systems represented by such models, however they are arrived at. The type of system we are interested in is a discrete-time or sampled-data system where the relation between input and output is (at least approximately) linear and where additive random dis turbances are also present, so that the behaviour of the system must be investigated by statistical methods. After a preliminary chapter summarizing elements of probability and linear system theory, we introduce in Chapter 2 some general linear stochastic models, both in input/output and state-space form. Chapter 3 concerns filtering theory: estimation of the state of a dynamical system from noisy observations. As well as being an important topic in its own right, filtering theory provides the link, via the so-called innovations representation, between input/output models (as identified by data analysis) and state-space models, as required for much contemporary control theory.
Author: Hong Wang Publisher: Springer Science & Business Media ISBN: 9781852331870 Category : Technology & Engineering Languages : en Pages : 196
Book Description
Over the past decades, although stochastic system control has been studied intensively within the field of control engineering, all the modelling and control strategies developed so far have concentrated on the performance of one or two output properties of the system. such as minimum variance control and mean value control. The general assumption used in the formulation of modelling and control strategies is that the distribution of the random signals involved is Gaussian. In this book, a set of new approaches for the control of the output probability density function of stochastic dynamic systems (those subjected to any bounded random inputs), has been developed. In this context, the purpose of control system design becomes the selection of a control signal that makes the shape of the system outputs p.d.f. as close as possible to a given distribution. The book contains material on the subjects of: - Control of single-input single-output and multiple-input multiple-output stochastic systems; - Stable adaptive control of stochastic distributions; - Model reference adaptive control; - Control of nonlinear dynamic stochastic systems; - Condition monitoring of bounded stochastic distributions; - Control algorithm design; - Singular stochastic systems. A new representation of dynamic stochastic systems is produced by using B-spline functions to descripe the output p.d.f. Advances in Industrial Control aims to report and encourage the transfer of technology in control engineering. The rapid development of control technology has an impact on all areas of the control discipline. The series offers an opportunity for researchers to present an extended exposition of new work in all aspects of industrial control.
Author: David D. Yao Publisher: Springer Science & Business Media ISBN: 0387217576 Category : Business & Economics Languages : en Pages : 472
Book Description
This books covers the broad range of research in stochastic models and optimization. Applications presented include networks, financial engineering, production planning, and supply chain management. Each contribution is aimed at graduate students working in operations research, probability, and statistics.
Author: Ivan Ivanov Publisher: BoD – Books on Demand ISBN: 9535108301 Category : Mathematics Languages : en Pages : 288
Book Description
Stochastic control plays an important role in many scientific and applied disciplines including communications, engineering, medicine, finance and many others. It is one of the effective methods being used to find optimal decision-making strategies in applications. The book provides a collection of outstanding investigations in various aspects of stochastic systems and their behavior. The book provides a self-contained treatment on practical aspects of stochastic modeling and calculus including applications drawn from engineering, statistics, and computer science. Readers should be familiar with basic probability theory and have a working knowledge of stochastic calculus. PhD students and researchers in stochastic control will find this book useful.
Author: Makiko Nisio Publisher: Springer ISBN: 4431551239 Category : Mathematics Languages : en Pages : 250
Book Description
This book offers a systematic introduction to the optimal stochastic control theory via the dynamic programming principle, which is a powerful tool to analyze control problems. First we consider completely observable control problems with finite horizons. Using a time discretization we construct a nonlinear semigroup related to the dynamic programming principle (DPP), whose generator provides the Hamilton–Jacobi–Bellman (HJB) equation, and we characterize the value function via the nonlinear semigroup, besides the viscosity solution theory. When we control not only the dynamics of a system but also the terminal time of its evolution, control-stopping problems arise. This problem is treated in the same frameworks, via the nonlinear semigroup. Its results are applicable to the American option price problem. Zero-sum two-player time-homogeneous stochastic differential games and viscosity solutions of the Isaacs equations arising from such games are studied via a nonlinear semigroup related to DPP (the min-max principle, to be precise). Using semi-discretization arguments, we construct the nonlinear semigroups whose generators provide lower and upper Isaacs equations. Concerning partially observable control problems, we refer to stochastic parabolic equations driven by colored Wiener noises, in particular, the Zakai equation. The existence and uniqueness of solutions and regularities as well as Itô's formula are stated. A control problem for the Zakai equations has a nonlinear semigroup whose generator provides the HJB equation on a Banach space. The value function turns out to be a unique viscosity solution for the HJB equation under mild conditions. This edition provides a more generalized treatment of the topic than does the earlier book Lectures on Stochastic Control Theory (ISI Lecture Notes 9), where time-homogeneous cases are dealt with. Here, for finite time-horizon control problems, DPP was formulated as a one-parameter nonlinear semigroup, whose generator provides the HJB equation, by using a time-discretization method. The semigroup corresponds to the value function and is characterized as the envelope of Markovian transition semigroups of responses for constant control processes. Besides finite time-horizon controls, the book discusses control-stopping problems in the same frameworks.
Author: M. H. A. Davis
Author: M. H. A. Davis
Author: Charles S. Tapiero
Author: Andreas Diekmann
Author: George Yin
Author: Mark Davis
Author: Hong Wang
Author: David D. Yao
Author: Ivan Ivanov
Author: Makiko Nisio
Author: Jacek Jakubowski