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Moderate deviations for the range of planar random walks
About this Title
Richard F. Bass, Xia Chen and Jay Rosen
Publication: Memoirs of the American Mathematical Society
Publication Year
:&Volume 198, Number 929
ISBNs: 978-0- (print); 978-1- (online)
DOI: http://dx.doi.org/10.1090/memo/0929MathSciNet review: MSC: Primary 60F10; Secondary 60G50, 60J55
Given a symmetric random walk in ${\mathbb
Z}^2$ with finite second moments, let $R_n$ be the range
of the random walk up to time $n$. The authors study moderate
deviations for $R_n -{\mathbb E}R_n$ and ${\mathbb E}R_n
-R_n$. They also derive the corresponding laws of the iterated
logarithm.
View other years and numbers:
Table of Contents
Chapter 1. Introduction
Chapter 2. History
Chapter 3. Overview
Chapter 4. Preliminaries
Chapter 5. Moments of the range
Chapter 6. Moderate deviations for $R_n - \mathbb {E}R_n$
Chapter 7. Moderate deviations for $\mathbb {E}R_n - R_n$
Chapter 8. Exponential asymptotics for the smoothed range
Chapter 9. Exponential approximation
Chapter 10. Laws of the iterated logarithmOptimal Hankel norm approximation for the Pritchard-Salamon class of infinite-dimensional systems | SpringerLink
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Optimal Hankel norm approximation for the Pritchard-Salamon class of infinite-dimensional systemsAmol J. SasaneRuth F. CurtainArticle
The optimal Hankel norm approximation problem is solved under the assumptions that the system Σ(A, B, C) is an exponentially stable, regular Pritchard-Salamon infinite-dimensional system. An explicit parameterization of all solutions is obtained in terms of the system parametersA, B, C.93C25 47N70 47A57 This is a preview of subscription content,
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∞-Control for Distributed Parameter Systems: A State-space Approach. Birkh?user, Boston, 1993.Amol J. Sasane1Ruth F. Curtain11.Department of MathematicsUniversity of GroningenGroningenThe NetherlandsFrequency-dependent polarization measurements of long-period surface waves and their implications for global phase-velocity maps - ScienceDirect
ExportJavaScript is disabled on your browser. Please enable JavaScript to use all the features on this page., July 1994, Pages 111-137Author links open overlay panelShow moreAbstractSurface-wave dispersion maps provide important constraints on global models of shear-wave velocity structure. Current surface-wave dispersion maps show significant differences from researcher to researcher, and it is clear that further work is required. In addition to dispersion data, polarization measurements obtained from long-period (100 s or more) three-component recordings from the various global networks can also be used to constrain dispersion maps. The off great circle propagation of the surface-wave packets is relatively easy to interpret within a ray-theoretic framework, and provides sensitivity to higher-order structure. The polarization angles as a function of frequency are readily measured using a multi-taper technique, which also has the benefit of providing an error estimate for the measurements. Application of the technique to three-component seismograms from the global GEOSCOPE array reveals large deviations from great circle propagation (up to 15° for low-orbit Love waves and 10° for Rayleigh waves in the frequency band 5–12.5 mHz). On a more regional scale, an analysis of seismograms from the German Regional Seismic Network (GRSN) reveals even larger, strongly frequency-dependent deviations from great circle propagation in the frequency range 10–50 mHz.Choose an option to locate/access this article:Check if you have access through your login credentials or your institution.ororRecommended articlesCiting articles (0)