Methods for Analysis of Switching Stochastic Systems PDF Download
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Author: Claes Jogréus
Publisher:
ISBN:
Category :
Languages : en
Pages : 115
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Book Description
Author: Claes Jogréus
Publisher:
ISBN:
Category :
Languages : en
Pages : 115
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Book Description
Author: El-Kébir Boukas
Publisher: Springer Science & Business Media
ISBN: 0817644520
Category : Technology & Engineering
Languages : en
Pages : 413
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Book Description
An introductory chapter highlights basics concepts and practical models, which are then used to solve more advanced problems throughout the book. Included are many numerical examples and LMI synthesis methods and design approaches.
Author: Allanus Hak-Man Tsoi
Publisher: World Scientific
ISBN: 9814355712
Category : Business & Economics
Languages : en
Pages : 274
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Book Description
Pt. I. Stochastic analysis and systems. 1. Multidimensional Wick-Ito formula for Gaussian processes / D. Nualart and S. Ortiz-Latorre. 2. Fractional white noise multiplication / A.H. Tsoi. 3. Invariance principle of regime-switching diffusions / C. Zhu and G. Yin -- pt. II. Finance and stochastics. 4. Real options and competition / A. Bensoussan, J.D. Diltz and S.R. Hoe. 5. Finding expectations of monotone functions of binary random variables by simulation, with applications to reliability, finance, and round robin tournaments / M. Brown, E.A. Pekoz and S.M. Ross. 6. Filtering with counting process observations and other factors : applications to bond price tick data / X. Hu, D.R. Kuipers and Y. Zeng. 7. Jump bond markets some steps towards general models in applications to hedging and utility problems / M. Kohlmann and D. Xiong. 8. Recombining tree for regime-switching model : algorithm and weak convergence / R.H. Liu. 9. Optimal reinsurance under a jump diffusion model / S. Luo. 10. Applications of counting processes and martingales in survival analysis / J. Sun. 11. Stochastic algorithms and numerics for mean-reverting asset trading / Q. Zhang, C. Zhuang and G. Yin
Author: Boris Brodsky
Publisher: CRC Press
ISBN: 1498755976
Category : Mathematics
Languages : en
Pages : 366
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Book Description
This book covers the development of methods for detection and estimation of changes in complex systems. These systems are generally described by nonstationary stochastic models, which comprise both static and dynamic regimes, linear and nonlinear dynamics, and constant and time-variant structures of such systems. It covers both retrospective and sequential problems, particularly theoretical methods of optimal detection. Such methods are constructed and their characteristics are analyzed both theoretically and experimentally. Suitable for researchers working in change-point analysis and stochastic modelling, the book includes theoretical details combined with computer simulations and practical applications. Its rigorous approach will be appreciated by those looking to delve into the details of the methods, as well as those looking to apply them.
Author: Tuan A. Hoang
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 0
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Book Description
This dissertation is concerned with the so-called stochastic hybrid systems, which are featured by the coexistence of continuous dynamics and discrete events and their interactions. Such systems have drawn much needed attentions in recent years. One of the main reasons is that such systems can be used to better reflect the reality for a wide range of applications in networked systems, communication systems, economic systems, cyber-physical systems, and biological and ecological systems, among others. Our main interest is centered around one class of such hybrid systems known as switching diffusions. In such a system, in addition to the driving force of a Brownian motion as in a stochastic system represented by a stochastic differential equation (SDE), there is an additional continuous-time switching process that models the environmental changes due to random events. In the first part, we develops numerical schemes for stochastic differential equations with Markovian switching (Markovian switching SDEs). By utilizing a special form of It̲o's formula for switching SDEs and special structural of the jumps of the switching component we derived a new scheme to simulate switching SDEs in the spirit of Milstein's scheme for purely SDEs. We also develop a new approach to establish the convergence of the proposed algorithm that incorporates martingale methods, quadratic variations, and Markovian stopping times. Detailed and delicate analysis is carried out. Under suitable conditions which are natural extensions of the classical ones, the convergence of the algorithms is established. The rate of convergence is also ascertained. The second part is concerned with a limit theorem for general stochastic differential equations with Markovian regime switching. Given a sequence of stochastic regime switching systems where the discrete switching processes are independent of the state of the systems. In the first part, we develops numerical schemes for stochastic differential equations with Markovian switching (Markovian switching SDEs). By utilizing a special form of Ito's formula for switching SDEs and special structural of the jumps of the switching component we derived a new scheme to simulate switching SDEs in the spirit of Milstein's scheme for purely SDEs. We also develop a new approach to establish the convergence of the proposed algorithm that incorporates martingale methods, quadratic variations, and Markovian stopping times. Detailed and delicate analysis is carried out. Under suitable conditions which are natural extensions of the classical ones, the convergence of the algorithms is established. The rate of convergence is also ascertained. The second part is concerned with a limit theorem for general stochastic differential equations with Markovian regime switching. Given a sequence of stochastic regime switching systems where the discrete switching processes are independent of the state of the systems. The continuous-state component of these systems are governed by stochastic differential equations with driving processes that are continuous increasing processes and square integrable martingales. We establish the convergence of the sequence of systems to the one described by a state independent regime-switching diffusion process when the two driving processes converge to the usual time process and the Brownian motion in suitable sense. The third part is concerned with controlled hybrid systems that are good approximations to controlled switching diffusion processes. In lieu of a Brownian motion noise, we use a wide-band noise formulation, which facilitates the treatment of non-Markovian models. The wide-band noise is one whose spectrum has band width wide enough. We work with a basic stationary mixing type process. On top of this wide-band noise process, we allow the system to be subject to random discrete event influence. The discrete event process is a continuous time Markov chain with a finite state space. Although the state space is finite, we assume that the state space is rather large and the Markov chain is irreducible. Using a two-time-scale formulation and assuming the Markov chain also subjects to fast variations, using weak convergence and singular perturbation test function method we first proved that the when controlled by nearly optimal and equilibrium controls, the state and the corresponding costs of the original systems would "converge" to those of controlled diffusions systems. Using the limit controlled dynamic system as a guidance, we construct controls for the original problem and show that the controls so constructed are near optimal and nearly equilibrium.
Author: Allanus Hak-Man Tsoi
Publisher: World Scientific
ISBN: 9814355704
Category : Mathematics
Languages : en
Pages : 274
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Book Description
This book introduces some advanced topics in probability theories ? both pure and applied ? is divided into two parts. The first part deals with the analysis of stochastic dynamical systems, in terms of Gaussian processes, white noise theory, and diffusion processes. The second part of the book discusses some up-to-date applications of optimization theories, martingale measure theories, reliability theories, stochastic filtering theories and stochastic algorithms towards mathematical finance issues such as option pricing and hedging, bond market analysis, volatility studies and asset trading modeling.
Author: Serguei Primak
Publisher: John Wiley & Sons
ISBN: 0470021179
Category : Technology & Engineering
Languages : en
Pages : 446
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Book Description
Stochastic Methods & their Applications to Communications presents a valuable approach to the modelling, synthesis and numerical simulation of random processes with applications in communications and related fields. The authors provide a detailed account of random processes from an engineering point of view and illustrate the concepts with examples taken from the communications area. The discussions mainly focus on the analysis and synthesis of Markov models of random processes as applied to modelling such phenomena as interference and fading in communications. Encompassing both theory and practice, this original text provides a unified approach to the analysis and generation of continuous, impulsive and mixed random processes based on the Fokker-Planck equation for Markov processes. Presents the cumulated analysis of Markov processes Offers a SDE (Stochastic Differential Equations) approach to the generation of random processes with specified characteristics Includes the modelling of communication channels and interfer ences using SDE Features new results and techniques for the of solution of the generalized Fokker-Planck equation Essential reading for researchers, engineers, and graduate and upper year undergraduate students in the field of communications, signal processing, control, physics and other areas of science, this reference will have wide ranging appeal.
Author: Vladimir S. Korolyuk
Publisher: Springer Science & Business Media
ISBN: 940114625X
Category : Mathematics
Languages : en
Pages : 195
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Book Description
In this monograph stochastic models of systems analysis are discussed. It covers many aspects and different stages from the construction of mathematical models of real systems, through mathematical analysis of models based on simplification methods, to the interpretation of real stochastic systems. The stochastic models described here share the property that their evolutionary aspects develop under the influence of random factors. It has been assumed that the evolution takes place in a random medium, i.e. unilateral interaction between the system and the medium. As only Markovian models of random medium are considered in this book, the stochastic models described here are determined by two processes, a switching process describing the evolution of the systems and a switching process describing the changes of the random medium. Audience: This book will be of interest to postgraduate students and researchers whose work involves probability theory, stochastic processes, mathematical systems theory, ordinary differential equations, operator theory, or mathematical modelling and industrial mathematics.
Author: Abdellah Benzaouia
Publisher: Springer Science & Business Media
ISBN: 1447128990
Category : Technology & Engineering
Languages : en
Pages : 300
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Book Description
Saturated Switching Systems treats the problem of actuator saturation, inherent in all dynamical systems by using two approaches: positive invariance in which the controller is designed to work within a region of non-saturating linear behaviour; and saturation technique which allows saturation but guarantees asymptotic stability. The results obtained are extended from the linear systems in which they were first developed to switching systems with uncertainties, 2D switching systems, switching systems with Markovian jumping and switching systems of the Takagi-Sugeno type. The text represents a thoroughly referenced distillation of results obtained in this field during the last decade. The selected tool for analysis and design of stabilizing controllers is based on multiple Lyapunov functions and linear matrix inequalities. All the results are illustrated with numerical examples and figures many of them being modelled using MATLAB®. Saturated Switching Systems will be of interest to academic researchers in control systems and to professionals working in any of the many fields where systems are affected by saturation including: chemical and pharmaceutical batch processing, manufacturing (for example in steel rolling), air-traffic control, and the automotive and aerospace industries.
Author: D. Kannan
Publisher: CRC Press
ISBN: 9780824706609
Category : Mathematics
Languages : en
Pages : 800
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Book Description
An introduction to general theories of stochastic processes and modern martingale theory. The volume focuses on consistency, stability and contractivity under geometric invariance in numerical analysis, and discusses problems related to implementation, simulation, variable step size algorithms, and random number generation.
