Those corresponding to majorants or minorants form the lower or upper part of of. The purpose of this note is to take a fresh look at some of groenebooms results in the context of path decompositions of williams 7, and to give a simple new description of this concave majorant. A minorant majorant approximation method for the solution of the nonlinear fourier equation. The positive minorant property on matrices the positive minorant property on matrices weissenhofer, s.
Let st be a version of the slope at time t of the concave majorant of brownian motion. On a majorantminorant criterion for the total preservation of global. In the process, we obtain an explicit version of lagrangebeltrami identity for ternary quadratic forms. We show that the l3 norm of f can be larger than that of f by a power of n. Acrobat reader dc ist mit adobe document cloud verbunden, damit du uberall. A matrix is said to be a majorant of another if all the entries in the first matrix are. For distributed controlled systems that can be represented by a functionaloperator equation of the hammerstein type with an additional term on the righthand side in the form of. The gaussnewtons method for solving nonlinear least squares problems is studied in this paper.
Download fulltext pdf download fulltext pdf a majorant problem article pdf available in international journal of mathematics and mathematical sciences 153 january 1992 with 21. In this connection, we develop an earlierproved majorantminorant criterion for the total preservation of. Characterizations of some stochastic processes wang, y. Keywords empirical distribution function concave majorant convex minorant. The positive minorant property on matrices sciencedirect. Since rn is almost surely asymptotic to, the construction shows that despite the equality of all of the onedimensional marginals, the almost sure behaviors of the sequences rn and fn may be radically different. Local convergence of newtons method under majorant. A minorantmajorant approximation method for the solution.
The limit distribution of the concave majorant of an. Pdf generalizations of the branch and bound method and of the piyavskii method for. If is a class of extended realvalued functions on a set d, a function. On matrix majorants and mlnorants, with applications to differential equations germund dahlquist. Minorant methods of stochastic global optimization. The positive minorant property on matrices, linear algebra. Pdfreader, pdfviewer kostenlos adobe acrobat reader dc. Infima of families of superharmonic functions springerlink. Download pdf 269 kb abstract in this paper we investigate a high dimensional version of selbergs minorant problem for the indicator function of an interval. Vertices of the least concave majorant of brownian motion with parabolic drift groeneboom, piet, electronic journal of probability, 2011. Abstractwe study the positive minorant property for norms on spaces of matrices. Download fulltext pdf on the minorant properties in c p h article pdf available in pacific journal of mathematics 1191 september 1985 with 24 reads. Recently groeneboom 1 studied the concave majorant process of a brownian motion b t, t.
A majorant method for nonlinear partial differential. Get a printable copy pdf file of the complete article 477k, or click on a page image below to. In chapter 1 we provide an overview of recent work on descriptions and properties of the convex minorant. We prove that a positive function on the unit disk admits a harmonic majorant if and only if a certain logarithmic lipschitz upper envelope of it relevant. For quadratic forms in up to 3 variables, we give an elementary and selfcontained proof of sylvesters criterion for positive definiteness as well as for nonnegative definiteness. In this paper, the proximal gaussnewton method for solving penalized nonlinear least squares problems is studied. A parametric family of linear differential systems with continuous coefficients bounded on the semiaxis and analytically dependent on a complex parameter is considered. It was shown in groeneboom 1983 that the least concave majorant of onesided brownian motion without drift can be characterized by a jump process with independent increments, which is the inverse of the process of slopes of the least concave majorant. Pdf minorant methods of stochastic global optimization. Statistics based on either concave majorants or convex minorants of.
The key concept of the minorant majorant optimization method is tangent. The key concept of the minorant majorant optimization method is tangent minorants majorants. We show that the difference of majorant and minorant. A local convergence analysis of newtons method for solving nonlinear equations, under a majorant condition, is presented in this paper. Convexconcave backtracking for inertial bregman proximal. A similar result is obtained in the 2samp1e case in which fa n is replaced by the slope of the convex minorant.
Estimation of local false discovery rates and higher. Full text full text is available as a scanned copy of the original print version. Local convergence analysis of gaussnewtons method under. Semicontinuity of majorants and minorants of lyapunovs. Best bounds for expected financial payoffs i algorithmic. Download fulltext pdf download fulltext pdf a majorant problem article pdf available in international journal of mathematics and mathematical sciences 153 january 1992 with 21 reads. Random walks whose concave majorants often have few. On the hardylittlewood majorant problem internet archive. Bounds for the triangular factors of a large matrix are given in terms of the triangular factors of an associated minorant. In the traditional setting, where the gradient of the smooth function gis lipschitz continuous, the majorant and the minorant.
Asymptotic normality of statistics based on the convex minorants of. Without assuming convexity of the derivative of the majorant. Abstracta systematic approach to the evaluation of best bounds for expected financial payoffs, in case the mean, variance and range of the distribution are known, is presented. The result is used to derive the asymptotic normality of certain statistics based on the concave majorants. Sylvesters minorant criterion, lagrangebeltrami identity. This provides a negative answer to a question, the hardy littlewood majorant. Weissenhofer department of mathematics and statistics the flinders university of south australia gpo box 2100 adelaide 5001, australia submitted by moshe goldberg abstract we study the positive minorant. N, the least superharmonic majorant greatest subharmonic minorant. Under the hypothesis that the derivative of the function associated with the least square problem satisfies a majorant. On matrix majorants and mlnorants, with applications to. Spitzers combinatorial lemma random walk convex hull convex minorant concave majorant. Similar examples could be constructed in which 3 is replaced by any p 2 not equal to an even integer.
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