225 research outputs found
Likelihood-based inference for a class of multivariate diffusions with unobserved paths
No full textThis document is the author's final manuscript accepted version of the journal article, incorporating any revisions agreed during the peer review process. Some differences between this version and the published version may remain. You are advised to consult the publisher's version if you wish to cite from it. Likelihood-based Inference for a Class of Multivariate Diffusions with Unobserved Paths Konstantinos Kalogeropoulos May 18, 2007 Abstract This paper presents a Markov chain Monte Carlo algorithm for a class of multivariate diffusion models with unobserved paths. This class is of high practical interest as it includes most diffusion driven stochastic volatility models. The algorithm is based on a data augmentation scheme where the paths are treated as missing data. However, unless these paths are transformed so that the dominating measure is independent of any parameters, the algorithm becomes reducible. The methodology developed in Roberts and Stramer (2001 Biometrika 88(3):603-621) circumvents the problem for scalar diffusions. We extend this framework to the class of models of this paper by introducing an appropriate reparametrisation of the likelihood that can be used to construct an irreducible data augmentation scheme. Practical implementation issues are considered and the methodology is applied to simulated data from the Heston model
Discretizing LTI descriptor (regular) differential input systems with consistent initial conditions
No full textA technique for discretizing efficiently the solution of a Linear descriptor (regular) differential input system with consistent initial conditions, and Time-Invariant coefficients (LTI) is introduced and fully discussed. Additionally an upper bound for the error ∥x(kT)-xk∥ that derives from the procedure of discretization is also provided. Practically speaking, we are interested in such kind of systems, since they are inherent in many physical, economical and engineering phenomena. Copyright © 2010 Athanasios D. Karageorgos et al
Solution properties of linear descriptor (Singular) matrix differential systems of higher order with (Non-) consistent initial conditions
No full textIn some interesting applications in control and system theory, linear descriptor (singular) matrix differential equations of higher order with time-invariant coefficients and (non-) consistent initial conditions have been used. In this paper, we provide a study for the solution properties of a more general class of the Apostol-Kolodner-type equations with consistent and nonconsistent initial conditions. © 2010 Athanasios A. Pantelous et al
The Drazin inverse through the matrix pencil approach and its application to the study of generalized linear systems with rectangular or square coefficient matrices
No full textIn several applications, e.g., in control and systems modeling theory, Drazin inverses and matrix pencil methods for the studyof generalized (descriptor) linear systems are used extensively. In this paper, a relation between the Drazin inverse and the Kronecker canonical form of rectangular pencils is derived and fullyin vestigated. Moreover, the relation between the Drazin inverse and the Weierstrass canonical form is revisited byp roviding a more algorithmic approach. Finally, the Weierstrass canonical form for a pencil through the core-nilpotent decomposition method is defined
An angle metric through the notion of Grassmann representative
No full textThe present paper has two main goals. Firstly, to introduce different metric topologies on the pencils (F,G) associated with autonomous singular (or regular) linear differential or difference systems. Secondly, to establish a new angle metric which is described by decomposable multi-vectors called Grassmann representatives (or Pl¨ucker coordinates) of the corresponding subspaces. A unified framework is provided by connecting the new results to known ones, thus aiding in the deeper understanding of various structural aspects of matrix pencils in system theory
Transferring instantly the state of higher-order linear descriptor (Regular) differential systems using impulsive inputs
No full textIn many applications, and generally speaking in many dynamical differential systems, the problem of transferring the initial state of the system to a desired state in (almost) zero-time time is desirable but difficult to achieve. Theoretically, this can be achieved by using a linear combination of Dirac δ -function and its derivatives. Obviously, such an input is physically unrealizable. However, we can think of it approximately as a combination of small pulses of very high magnitude and infinitely small duration. In this paper, the approximation process of the distributional behaviour of higher-order linear descriptor (regular) differential systems is presented. Thus, new analytical formulae based on linear algebra methods and generalized inverses theory are provided. Our approach is quite general and some significant conditions are derived. Finally, a numerical example is presented and discussed. © 2009 Athanasios D. Karageorgos et al
Symmetric/skew-symmetric homogeneous matrix descriptor (regular) differential systems with consistent initial conditions
No full textPower series solutions for linear higher order rectangular differential matrix control systems
No full textPower series solutions for linear higher order rectangular differential matrix control systems
No full textThis paper is concerned with the solution of linear higher order rectangular differential matrix systems which are appeared in many applications of optimal and filtering control theory. The classical power series method is employed to obtain the analytic solution of linear higher order rectangular (singular) differential matrix equations. In the present paper, the authors provide some preliminary results for solving linear singular matrix systems with the power series approach
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