Download or read book Analysis of Bilinear Stochastic Systems written by Alan S. Willsky and published by . This book was released on 1974 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Bilinear Stochastic Models and Related Problems of Nonlinear Time Series Analysis written by György Terdik and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: The object of the present work is a systematic statistical analysis of bilinear processes in the frequency domain. The first two chapters are devoted to the basic theory of nonlinear functions of stationary Gaussian processes, Hermite polynomials, cumulants and higher order spectra, multiple Wiener-Itô integrals and finally chaotic Wiener-Itô spectral representation of subordinated processes. There are two chapters for general nonlinear time series problems.
Download or read book Estimation and Analysis of Nonlinear Stochastic Systems written by Steven Irl Marcus and published by . This book was released on 1975 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: The algebraic and geometric structure of certain classes of nonlinear stochastic systems is exploited in order to obtain useful stability and estimation results. First, the class of bilinear stochastic systems (or linear systems with multiplicative noise) is discussed. The stochastic stability of bilinear systems driven by colored noise is considered; in the case that the system evolves on a solvable Lie group, necessary and sufficient conditions for stochastic stability are derived. Approximate methods for obtaining sufficient conditions for the stochastic stability of bilinear systems evolving on general Lie groups are also discussed. The study of estimation problems involving bilinear systems is motivated by several practical applications involving rotational processes in three dimensions. Two classes of estimation problems are considered. First it is proved that, for systems described by certain types of Volterra series expansions or by certain bilinear equations evolving on nilpotent or solvable Lie groups, the optimal conditional mean estimator consists of a finite dimensional nonlinear set of equations. Finally, the theory of harmonic analysis is used to derive suboptimal estimators for bilinear systems driven by white noise which evolve on compact Lie groups or homogeneous spaces.
Download or read book Stability and Control Analysis of Stochastic Bilinear Systems written by Philip L. Wing and published by . This book was released on 1994 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On the Stability of Bilinear Stochastic Systems written by Bernard Delyon and published by . This book was released on 1988 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Modeling and Estimation with Bilinear Stochastic Systems written by Roger W. Brockett and published by . This book was released on 1979 with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Estimation for Bilinear Stochastic Systems written by Alan S. Willsky and published by . This book was released on 1974 with total page 59 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Modelling and Application of Stochastic Processes written by Uday B. Desai and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of modelling and application of stochastic processes is too vast to be exhausted in a single volume. In this book, attention is focused on a small subset of this vast subject. The primary emphasis is on realization and approximation of stochastic systems. Recently there has been considerable interest in the stochastic realization problem, and hence, an attempt has been made here to collect in one place some of the more recent approaches and algorithms for solving the stochastic realiza tion problem. Various different approaches for realizing linear minimum-phase systems, linear nonminimum-phase systems, and bilinear systems are presented. These approaches range from time-domain methods to spectral-domain methods. An overview of the chapter contents briefly describes these approaches. Also, in most of these chapters special attention is given to the problem of developing numerically ef ficient algorithms for obtaining reduced-order (approximate) stochastic realizations. On the application side, chapters on use of Markov random fields for modelling and analyzing image signals, use of complementary models for the smoothing problem with missing data, and nonlinear estimation are included. Chapter 1 by Klein and Dickinson develops the nested orthogonal state space realization for ARMA processes. As suggested by the name, nested orthogonal realizations possess two key properties; (i) the state variables are orthogonal, and (ii) the system matrices for the (n + l)st order realization contain as their "upper" n-th order blocks the system matrices from the n-th order realization (nesting property).
Download or read book Bilinear Stochastic Models and Related Problems of Nonlinear Time Series Analysis written by Gyorgy Terdik and published by . This book was released on 1999-07-30 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: The object of the present work is a systematic statistical analysis of bilinear processes in the frequency domain. The first two chapters are devoted to the basic theory of nonlinear functions of stationary Gaussian processes, Hermite polynomials, cumulants and higher order spectra, multiple Wiener-ItA integrals and finally chaotic Wiener-ItA spectral representation of subordinated processes. There are two chapters for general nonlinear time series problems.
Download or read book Bilinear Stochastic Processes and Time Series written by Zhigiang Tang and published by . This book was released on 1987 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: In engineering, biology, ecology, medicine, economics and social science, some processes are essentially bilinear, and some could be approximated accurately by bilinear processes under certain conditions. In this thesis the bilinear stochastic process and bilinear time series are discussed. Bilinear models essentially are nonlinear; the superposition rule is not valid. A useful property, which characterizes the bilinear feature among the nonlinear ones, is emphasized. The solutions of deterministic bilinear systems and bilinear stochastic processes are given. The direct method uses the Lie algebraic structure. For bilinear stochastic processes, the decomposition to a cascade form is a generalization of the Volterra-series expansion. Because a correction term exists in bilinear stochastic differential equations, the decomposition has two different forms; both of them are convergent. The lth -order stationarity and asymptotic stationarity of bilinear stochastic processes and time series are well defined, and the conditions on parameters for lth -order stationarity are derived. Affine bilinear models in time-series form are shown to be more general than bilinear models, and more readily fit certain data. A special high-order scalar affine bilinear time-series model can be transferred to a first-order, vector, affine, bilinear model, but need higher dimension than the linear ARMA model. For first-order affine bilinear time series two possible methods of parameter estimation are presented. The moment method uses the relationships between the parameters, and the second and third-moments to estimate parameters. The inverse method uses the output data to estimate the input, which is compared with the standard white Gaussian random sequence, and the method chooses the parameters of the model to make certain criterion optimal. For the general non-Gaussian time series an identification procedure using the inverse method is proposed. Some examples of analysis and parameter estimation of bilinear models are provided.
Download or read book Stochastic Differential and Difference Equations written by Imre Csiszár and published by Springer Science & Business Media. This book was released on 1997 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Periodically Correlated Solutions to a Class of Stochastic Difference Equations.- On Nonlinear SDE'S whose Densities Evolve in a Finite-Dimensional Family.- Composition of Skeletons and Support Theorems.- Invariant Measure for a Wave Equation on a Riemannian Manifold.- Ergodic Distributed Control for Parameter Dependent Stochastic Semilinear Systems.- Dirichlet Forms, Caccioppoli Sets and the Skorohod Equation Masatoshi Fukushima.- Rate of Convergence of Moments of Spall's SPSA Method.- General Setting for Stochastic Processes Associated with Quantum Fields.- On a Class of Semilinear Stochastic Partial Differential Equations.- Parallel Numerical Solution of a Class of Volterra Integro-Differential Equations.- On the Laws of the Oseledets Spaces of Linear Stochastic Differential Equations.- On Stationarity of Additive Bilinear State-space Representation of Time Series.- On Convergence of Approximations of Ito-Volterra Equations.- Non-isotropic Ornstein-Uhlenbeck Process and White Noise Analysis.- Stochastic Processes with Independent Increments on a Lie Group and their Selfsimilar Properties.- Optimal Damping of Forced Oscillations Discrete-time Systems by Output Feedback.- Forecast of Lévy's Brownian Motion as the Observation Domain Undergoes Deformation.- A Maximal Inequality for the Skorohod Integral.- On the Kinematics of Stochastic Mechanics.- Stochastic Equations in Formal Mappings.- On Fisher's Information Matrix of an ARMA Process.- Statistical Analysis of Nonlinear and NonGaussian Time Series.- Bilinear Stochastic Systems with Long Range Dependence in Continuous Time.- On Support Theorems for Stochastic Nonlinear Partial Differential Equations.- Excitation and Performance in Continuous-time Stochastic Adaptive LQ-control.- Invariant Measures for Diffusion Processes in Conuclear Spaces.- Degree Theory on Wiener Space and an Application to a Class of SPDEs.- On the Interacting Measure-Valued Branching Processes.
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1989 with total page 1134 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Energy Estimates and Model Order Reduction for Stochastic Bilinear Systems written by Martin Redmann and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we investigate a large-scale stochastic system with bilinear drift and linear diffusion term. Such high dimensional systems appear for example when discretizing a stochastic partial differential equations in space. We study a particular model order reduction technique called balanced truncation (BT) to reduce the order of spatially-discretized systems and hence reduce computational complexity. We introduce suitable Gramians to the system and prove energy estimates that can be used to identify states which contribute only very little to the system dynamics. When BT is applied the reduced system is obtained by removing these states from the original system. The main contribution of this paper is an L2-error bound for BT for stochastic bilinear systems. This result is new even for deterministic bilinear equations. In order to achieve it, we develop a new technique which is not available in the literature so far.
Download or read book Bilinear Control Systems written by David Elliott and published by Springer Science & Business Media. This book was released on 2009-09-01 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: The mathematical theory of control became a ?eld of study half a century ago in attempts to clarify and organize some challenging practical problems and the methods used to solve them. It is known for the breadth of the mathematics it uses and its cross-disciplinary vigor. Its literature, which can befoundinSection93ofMathematicalReviews,wasatonetimedominatedby the theory of linear control systems, which mathematically are described by linear di?erential equations forced by additive control inputs. That theory led to well-regarded numerical and symbolic computational packages for control analysis and design. Nonlinear control problems are also important; in these either the - derlying dynamical system is nonlinear or the controls are applied in a n- additiveway.Thelastfourdecadeshaveseenthedevelopmentoftheoretical work on nonlinear control problems based on di?erential manifold theory, nonlinear analysis, and several other mathematical disciplines. Many of the problems that had been solved in linear control theory, plus others that are new and distinctly nonlinear, have been addressed; some resulting general de?nitions and theorems are adapted in this book to the bilinear case.
Download or read book Bilinear State Space Realization for Polynomial Stochastic Systems written by György Terdik and published by . This book was released on 1989 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Stochastic Processes Modeling and Simulation written by D N Shanbhag and published by Gulf Professional Publishing. This book was released on 2003-02-24 with total page 1028 pages. Available in PDF, EPUB and Kindle. Book excerpt: This sequel to volume 19 of Handbook on Statistics on Stochastic Processes: Modelling and Simulation is concerned mainly with the theme of reviewing and, in some cases, unifying with new ideas the different lines of research and developments in stochastic processes of applied flavour. This volume consists of 23 chapters addressing various topics in stochastic processes. These include, among others, those on manufacturing systems, random graphs, reliability, epidemic modelling, self-similar processes, empirical processes, time series models, extreme value therapy, applications of Markov chains, modelling with Monte Carlo techniques, and stochastic processes in subjects such as engineering, telecommunications, biology, astronomy and chemistry. particular with modelling, simulation techniques and numerical methods concerned with stochastic processes. The scope of the project involving this volume as well as volume 19 is already clarified in the preface of volume 19. The present volume completes the aim of the project and should serve as an aid to students, teachers, researchers and practitioners interested in applied stochastic processes.
Download or read book Stochastic Bilinear Systems written by G. Koch and published by . This book was released on 1972 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
