Download or read book Random Integral Equations with Applications to Stochastic Systems written by C. P. Tsokos and published by Springer. This book was released on 2006-11-15 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors have two main objectives in these notes. First, they wish to give a complete presentation of the theory of existence and uniqueness of random solutions of the most general random Volterra and Fredholm equations which have been studied heretofore. Second, to emphasize the application of their theory to stochastic systems which have not been extensively studied before due to mathematical difficulties that arise. These notes will be of value to mathematicians, probabilists, and engineers who are working in the area of systems theory or to those who are interested in the theory of random equations.
Download or read book Random Integral Equations with Applications to Stochastic Systems written by C. P. Tsokos and published by . This book was released on 2014-01-15 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Random Integral Equations with Applications to Stochastic Systems written by Chris P. Tsokos and published by Springer. This book was released on 1971-01-01 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Random integral equations with applications to stochastic systems written by Chris P. Toskos and published by . This book was released on 1971 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Random Integral Equations with Applications to Stochastic Systems written by Aldo Andreotti and published by . This book was released on 1971 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Random Integral Equations with Applications to Stochastic System written by Chris P. Tsokos and published by . This book was released on 1971 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Approximation and Weak Convergence Methods for Random Processes with Applications to Stochastic Systems Theory written by Harold Joseph Kushner and published by MIT Press. This book was released on 1984 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Control and communications engineers, physicists, and probability theorists, among others, will find this book unique. It contains a detailed development of approximation and limit theorems and methods for random processes and applies them to numerous problems of practical importance. In particular, it develops usable and broad conditions and techniques for showing that a sequence of processes converges to a Markov diffusion or jump process. This is useful when the natural physical model is quite complex, in which case a simpler approximation la diffusion process, for example) is usually made. The book simplifies and extends some important older methods and develops some powerful new ones applicable to a wide variety of limit and approximation problems. The theory of weak convergence of probability measures is introduced along with general and usable methods (for example, perturbed test function, martingale, and direct averaging) for proving tightness and weak convergence. Kushner's study begins with a systematic development of the method. It then treats dynamical system models that have state-dependent noise or nonsmooth dynamics. Perturbed Liapunov function methods are developed for stability studies of nonMarkovian problems and for the study of asymptotic distributions of non-Markovian systems. Three chapters are devoted to applications in control and communication theory (for example, phase-locked loops and adoptive filters). Smallnoise problems and an introduction to the theory of large deviations and applications conclude the book. Harold J. Kushner is Professor of Applied Mathematics and Engineering at Brown University and is one of the leading researchers in the area of stochastic processes concerned with analysis and synthesis in control and communications theory. This book is the sixth in The MIT Press Series in Signal Processing, Optimization, and Control, edited by Alan S. Willsky.
Download or read book Stochastic Systems Theory And Applications written by V S Pugachev and published by World Scientific Publishing Company. This book was released on 2002-01-02 with total page 930 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the general theory and basic methods of linear and nonlinear stochastic systems (StS) i.e. dynamical systems described by stochastic finite- and infinite-dimensional differential, integral, integrodifferential, difference etc equations. The general StS theory is based on the equations for characteristic functions and functionals. The book outlines StS structural theory, including direct numerical methods, methods of normalization, equivalent linearization and parametrization of one- and multi-dimensional distributions, based on moments, quasimoments, semi-invariants and orthogonal expansions. Special attention is paid to methods based on canonical expansions and integral canonical representations. About 500 exercises and problems are provided. The authors also consider applications in mathematics and mechanics, physics and biology, control and information processing, operations research and finance.
Download or read book Random Integral Equations with Applications to Life Sciences and Engineering written by and published by Academic Press. This book was released on 1974-08-20 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; andmethods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.As a result, the book represents a blend of new methods in general computational analysis,and specific, but also generic, techniques for study of systems theory ant its particularbranches, such as optimal filtering and information compression. - Best operator approximation,- Non-Lagrange interpolation,- Generic Karhunen-Loeve transform- Generalised low-rank matrix approximation- Optimal data compression- Optimal nonlinear filtering
Download or read book Random Integral Equations written by Bharucha-Reid and published by Academic Press. This book was released on 1973-03-02 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: Random Integral Equations
Download or read book Stochastic Calculus written by Mircea Grigoriu and published by Springer Science & Business Media. This book was released on 2013-12-11 with total page 784 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic, differential, and integral equations are used in the applied sciences, en gineering, economics, and the social sciences to characterize the current state of a physical, economic, or social system and forecast its evolution in time. Generally, the coefficients of and/or the input to these equations are not precisely known be cause of insufficient information, limited understanding of some underlying phe nomena, and inherent randonmess. For example, the orientation of the atomic lattice in the grains of a polycrystal varies randomly from grain to grain, the spa tial distribution of a phase of a composite material is not known precisely for a particular specimen, bone properties needed to develop reliable artificial joints vary significantly with individual and age, forces acting on a plane from takeoff to landing depend in a complex manner on the environmental conditions and flight pattern, and stock prices and their evolution in time depend on a large number of factors that cannot be described by deterministic models. Problems that can be defined by algebraic, differential, and integral equations with random coefficients and/or input are referred to as stochastic problems. The main objective of this book is the solution of stochastic problems, that is, the determination of the probability law, moments, and/or other probabilistic properties of the state of a physical, economic, or social system. It is assumed that the operators and inputs defining a stochastic problem are specified.
Download or read book Random Ordinary Differential Equations and Their Numerical Solution written by Xiaoying Han and published by Springer. This book was released on 2017-10-25 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended to make recent results on the derivation of higher order numerical schemes for random ordinary differential equations (RODEs) available to a broader readership, and to familiarize readers with RODEs themselves as well as the closely associated theory of random dynamical systems. In addition, it demonstrates how RODEs are being used in the biological sciences, where non-Gaussian and bounded noise are often more realistic than the Gaussian white noise in stochastic differential equations (SODEs). RODEs are used in many important applications and play a fundamental role in the theory of random dynamical systems. They can be analyzed pathwise with deterministic calculus, but require further treatment beyond that of classical ODE theory due to the lack of smoothness in their time variable. Although classical numerical schemes for ODEs can be used pathwise for RODEs, they rarely attain their traditional order since the solutions of RODEs do not have sufficient smoothness to have Taylor expansions in the usual sense. However, Taylor-like expansions can be derived for RODEs using an iterated application of the appropriate chain rule in integral form, and represent the starting point for the systematic derivation of consistent higher order numerical schemes for RODEs. The book is directed at a wide range of readers in applied and computational mathematics and related areas as well as readers who are interested in the applications of mathematical models involving random effects, in particular in the biological sciences.The level of this book is suitable for graduate students in applied mathematics and related areas, computational sciences and systems biology. A basic knowledge of ordinary differential equations and numerical analysis is required.
Download or read book Stochastic Differential Equations and Applications written by X Mao and published by Elsevier. This book was released on 2007-12-30 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: This advanced undergraduate and graduate text has now been revised and updated to cover the basic principles and applications of various types of stochastic systems, with much on theory and applications not previously available in book form. The text is also useful as a reference source for pure and applied mathematicians, statisticians and probabilists, engineers in control and communications, and information scientists, physicists and economists. Has been revised and updated to cover the basic principles and applications of various types of stochastic systems Useful as a reference source for pure and applied mathematicians, statisticians and probabilists, engineers in control and communications, and information scientists, physicists and economists
Download or read book Random Evolutions and Their Applications written by Anatoly Swishchuk and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main purpose of this handbook is to summarize and to put in order the ideas, methods, results and literature on the theory of random evolutions and their applications to the evolutionary stochastic systems in random media, and also to present some new trends in the theory of random evolutions and their applications. In physical language, a random evolution ( RE ) is a model for a dynamical sys tem whose state of evolution is subject to random variations. Such systems arise in all branches of science. For example, random Hamiltonian and Schrodinger equations with random potential in quantum mechanics, Maxwell's equation with a random refractive index in electrodynamics, transport equations associated with the trajec tory of a particle whose speed and direction change at random, etc. There are the examples of a single abstract situation in which an evolving system changes its "mode of evolution" or "law of motion" because of random changes of the "environment" or in a "medium". So, in mathematical language, a RE is a solution of stochastic operator integral equations in a Banach space. The operator coefficients of such equations depend on random parameters. Of course, in such generality , our equation includes any homogeneous linear evolving system. Particular examples of such equations were studied in physical applications many years ago. A general mathematical theory of such equations has been developed since 1969, the Theory of Random Evolutions.
Download or read book Stochastic Differential Equations written by K. Sobczyk and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'Et moi, ..~ si lavait su CO.llUlJalt en revc:nir, One acMcc matbcmatica bu JaIdcred the human rac:c. It bu put COIDIDOD _ beet je n'y serais point aBe.' Jules Verne wbac it bdoup, 0Jl!be~ IbcII _t to!be dusty cauialcr Iabc & d 'diMardod__ The series is divergent; thc:reforc we may be -'. I!.ticT. Bc:I1 able to do something with it. O. Hcavisidc Mathematics is a tool for thought. A highly necessary tool in a world when: both feedback and non linearities abound. Similarly. all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statcmalts as: 'One service topology has rendered mathematical physics ...-; 'One service logic has rendered c0m puter science ... '; 'One service category theory has rendered mathematics ... '. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series. This series, Mathematics and Its Applications. started in 19n. Now that over one hundred volumes have appeared it seems opportune to reexamine its scope. At the time I wrote "Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However. the 'tree' of knowledge of mathematics and related fields does not grow only by putting forth new branc:hes. It also happens, quite often in fact, that branches which were thought to be completely
Download or read book Stochastic Differential Equations and Applications written by Avner Friedman and published by Academic Press. This book was released on 2014-06-20 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic Differential Equations and Applications, Volume 1 covers the development of the basic theory of stochastic differential equation systems. This volume is divided into nine chapters. Chapters 1 to 5 deal with the basic theory of stochastic differential equations, including discussions of the Markov processes, Brownian motion, and the stochastic integral. Chapter 6 examines the connections between solutions of partial differential equations and stochastic differential equations, while Chapter 7 describes the Girsanov’s formula that is useful in the stochastic control theory. Chapters 8 and 9 evaluate the behavior of sample paths of the solution of a stochastic differential system, as time increases to infinity. This book is intended primarily for undergraduate and graduate mathematics students.
Download or read book Random Evolutions and their Applications written by Anatoly Swishchuk and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to the new trends in random evolutions and their various applications to stochastic evolutionary sytems (SES). Such new developments as the analogue of Dynkin's formulae, boundary value problems, stochastic stability and optimal control of random evolutions, stochastic evolutionary equations driven by martingale measures are considered. The book also contains such new trends in applied probability as stochastic models of financial and insurance mathematics in an incomplete market. In the famous classical financial mathematics Black-Scholes model of a (B,S) market for securities prices, which is used for the description of the evolution of bonds and stocks prices and also for their derivatives, such as options, futures, forward contracts, etc., it is supposed that the dynamic of bonds and stocks prices are set by a linear differential and linear stochastic differential equations, respectively, with interest rate, appreciation rate and volatility such that they are predictable processes. Also, in the Arrow-Debreu economy, the securities prices which support a Radner dynamic equilibrium are a combination of an Ito process and a random point process, with the all coefficients and jumps being predictable processes.
