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Author

Pavel Chigansky

Other affiliations: Weizmann Institute of Science
Bio: Pavel Chigansky is an academic researcher from Hebrew University of Jerusalem. The author has contributed to research in topics: Fractional Brownian motion & Markov chain. The author has an hindex of 14, co-authored 65 publications receiving 707 citations. Previous affiliations of Pavel Chigansky include Weizmann Institute of Science.


Papers
More filters
Journal ArticleDOI
TL;DR: A necessary condition for stability under arbitrary switching is that every matrix in the convex hull of the matrices defining the subsystems is Hurwitz, and it is shown that np = 3.
Abstract: We consider n-dimensional positive linear switched systems. A necessary condition for stability under arbitrary switching is that every matrix in the convex hull of the matrices defining the subsystems is Hurwitz. Several researchers conjectured that for positive linear switched systems this condition is also sufficient. Recently, Gurvits, Shorten, and Mason showed that this conjecture is true for the case n = 2, but is not true in general. Their results imply that there exists some minimal integer np such that the conjecture is true for all n < np, but is not true for n = np. We show that np = 3.

188 citations

Journal ArticleDOI
TL;DR: The stability problem of the Wonham filter with respect to initial conditions is addressed, and new bounds for the exponential stability rates, which do not depend on the observations are given.
Abstract: The stability problem of the Wonham filter with respect to initial conditions is addressed. The case of ergodic signals is revisited in view of a gap in the classic work of H. Kunita (1971). We give new bounds for the exponential stability rates, which do not depend on the observations. In the nonergodic case, the stability is implied by identifiability conditions, formulated explicitly in terms of the transition intensities matrix and the observation structure.

56 citations

Posted Content
TL;DR: In this article, the stability of the Wonham filter with respect to initial conditions is studied in terms of the transition intensities matrix and the observation structure, and new bounds for the exponential stability rates do not depend on the observations.
Abstract: Stability problem of the Wonham filter with respect to initial conditions is addressed. The case of ergodic signals is revisited in view of a gap in the classic work of H. Kunita (1971). We give new bounds for the exponential stability rates, which do not depend on the observations. In the non-ergodic case, the stability is implied by identifiability conditions, formulated explicitly in terms of the transition intensities matrix and the observation structure.

41 citations

Journal ArticleDOI
TL;DR: In this paper, it is shown that the mixing condition might be relaxed regardless of an observation process structure, regardless of the signal ergodicity of the input signal and the transition probability density of the incoming signal.
Abstract: The nonlinear filtering equation is said to be stable if it ``forgets'' the initial condition. It is known that the filter might be unstable even if the signal is an ergodic Markov chain. In general, the filtering stability requires stronger signal ergodicity provided by the, so called, mixing condition. The latter is formulated in terms of the transition probability density of the signal. The most restrictive requirement of the mixing condition is the uniform positiveness of this density. We show that it might be relaxed regardless of an observation process structure.

39 citations

Journal ArticleDOI
TL;DR: In this article, a new canonical innovation representation for mixed processes was obtained using linear filtering theory, which generalizes the classical innovation formulas beyond the square integrable setting and is applicable to processes with additional fractional structure.
Abstract: This paper presents a new approach to the analysis of mixed processes \[X_{t}=B_{t}+G_{t},\qquad t\in[0,T],\] where $B_{t}$ is a Brownian motion and $G_{t}$ is an independent centered Gaussian process. We obtain a new canonical innovation representation of $X$, using linear filtering theory. When the kernel \[K(s,t)=\frac{\partial^{2}}{\partial s\,\partial t}\mathbb{E}G_{t}G_{s},\qquad s e t\] has a weak singularity on the diagonal, our results generalize the classical innovation formulas beyond the square integrable setting. For kernels with stronger singularity, our approach is applicable to processes with additional “fractional” structure, including the mixed fractional Brownian motion from mathematical finance. We show how previously-known measure equivalence relations and semimartingale properties follow from our canonical representation in a unified way, and complement them with new formulas for Radon–Nikodym densities.

37 citations


Cited by
More filters
Journal ArticleDOI
TL;DR: This handbook is a very useful handbook for engineers, especially those working in signal processing, and provides real data bootstrap applications to illustrate the theory covered in the earlier chapters.
Abstract: tions. Bootstrap has found many applications in engineering field, including artificial neural networks, biomedical engineering, environmental engineering, image processing, and radar and sonar signal processing. Basic concepts of the bootstrap are summarized in each section as a step-by-step algorithm for ease of implementation. Most of the applications are taken from the signal processing literature. The principles of the bootstrap are introduced in Chapter 2. Both the nonparametric and parametric bootstrap procedures are explained. Babu and Singh (1984) have demonstrated that in general, these two procedures behave similarly for pivotal (Studentized) statistics. The fact that the bootstrap is not the solution for all of the problems has been known to statistics community for a long time; however, this fact is rarely touched on in the manuscripts meant for practitioners. It was first observed by Babu (1984) that the bootstrap does not work in the infinite variance case. Bootstrap Techniques for Signal Processing explains the limitations of bootstrap method with an example. I especially liked the presentation style. The basic results are stated without proofs; however, the application of each result is presented as a simple step-by-step process, easy for nonstatisticians to follow. The bootstrap procedures, such as moving block bootstrap for dependent data, along with applications to autoregressive models and for estimation of power spectral density, are also presented in Chapter 2. Signal detection in the presence of noise is generally formulated as a testing of hypothesis problem. Chapter 3 introduces principles of bootstrap hypothesis testing. The topics are introduced with interesting real life examples. Flow charts, typical in engineering literature, are used to aid explanations of the bootstrap hypothesis testing procedures. The bootstrap leads to second-order correction due to pivoting; this improvement in the results due to pivoting is also explained. In the second part of Chapter 3, signal processing is treated as a regression problem. The performance of the bootstrap for matched filters as well as constant false-alarm rate matched filters is also illustrated. Chapters 2 and 3 focus on estimation problems. Chapter 4 introduces bootstrap methods used in model selection. Due to the inherent structure of the subject matter, this chapter may be difficult for nonstatisticians to follow. Chapter 5 is the most impressive chapter in the book, especially from the standpoint of statisticians. It provides real data bootstrap applications to illustrate the theory covered in the earlier chapters. These include applications to optimal sensor placement for knock detection and land-mine detection. The authors also provide a MATLAB toolbox comprising frequently used routines. Overall, this is a very useful handbook for engineers, especially those working in signal processing.

1,292 citations

Book
01 Jan 1966
TL;DR: Boundary value problems in physics and engineering were studied in this article, where Chorlton et al. considered boundary value problems with respect to physics, engineering, and computer vision.
Abstract: Boundary Value Problems in Physics and Engineering By Frank Chorlton. Pp. 250. (Van Nostrand: London, July 1969.) 70s

733 citations

Journal ArticleDOI
TL;DR: The stability analysis problem for a class of switched positive linear systems (SPLSs) with average dwell time switching is investigated and a multiple linear copositive Lyapunov function is introduced, by which the sufficient stability criteria are given for the underlying systems in both continuous-time and discrete-time contexts.

597 citations

Journal ArticleDOI
TL;DR: Two classes of state feedback controllers and a common Lyapunov function (CLF) are simultaneously constructed by backstepping to solve the global stabilization problem for switched nonlinear systems in lower triangular form under arbitrary switchings.

404 citations