The positive minorant property on matrices, linear algebra. Vertices of the least concave majorant of brownian motion with parabolic drift groeneboom, piet, electronic journal of probability, 2011. Estimation of local false discovery rates and higher. A matrix is said to be a majorant of another if all the entries in the first matrix are. A minorantmajorant approximation method for the solution. 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. 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. 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. On a majorantminorant criterion for the total preservation of global. The limit distribution of the concave majorant of an. Pdf minorant methods of stochastic global optimization. A parametric family of linear differential systems with continuous coefficients bounded on the semiaxis and analytically dependent on a complex parameter is considered.
Those corresponding to majorants or minorants form the lower or upper part of of. Acrobat reader dc ist mit adobe document cloud verbunden, damit du uberall. Local convergence analysis of gaussnewtons method under. 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. 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.
Let st be a version of the slope at time t of the concave majorant of brownian motion. The positive minorant property on matrices sciencedirect. Asymptotic normality of statistics based on the convex minorants of. The key concept of the minorant majorant optimization method is tangent minorants majorants. Spitzers combinatorial lemma random walk convex hull convex minorant concave majorant. N, the least superharmonic majorant greatest subharmonic minorant. Without assuming convexity of the derivative of the majorant. Convexconcave backtracking for inertial bregman proximal. In this paper, the proximal gaussnewton method for solving penalized nonlinear least squares problems is studied. 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.
In the process, we obtain an explicit version of lagrangebeltrami identity for ternary quadratic forms. Minorant methods of stochastic global optimization. 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. The positive minorant property on matrices the positive minorant property on matrices weissenhofer, s. 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. A similar result is obtained in the 2samp1e case in which fa n is replaced by the slope of the convex minorant. In the traditional setting, where the gradient of the smooth function gis lipschitz continuous, the majorant and the minorant. A minorant majorant approximation method for the solution of the nonlinear fourier equation. In this connection, we develop an earlierproved majorantminorant criterion for the total preservation of.
A majorant method for nonlinear partial differential. Statistics based on either concave majorants or convex minorants of. 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. Characterizations of some stochastic processes wang, y. Keywords empirical distribution function concave majorant convex minorant. Majorant problems for fourier coefficients, the quarterly journal of mathematics, volume 26, issue 1, 1 january 1975, pages 918. If is a class of extended realvalued functions on a set d, a function. Sylvesters minorant criterion, lagrangebeltrami identity. Full text full text is available as a scanned copy of the original print version. 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. Under the hypothesis that the derivative of the function associated with the least square problem satisfies a majorant. Pdf generalizations of the branch and bound method and of the piyavskii method for. 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. Random walks whose concave majorants often have few.
The key concept of the minorant majorant optimization method is tangent. Best bounds for expected financial payoffs i algorithmic. We show that the l3 norm of f can be larger than that of f by a power of n. 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. A local convergence analysis of newtons method for solving nonlinear equations, under a majorant condition, is presented in this paper. The result is used to derive the asymptotic normality of certain statistics based on the concave majorants. In chapter 1 we provide an overview of recent work on descriptions and properties of the convex minorant. Recently groeneboom 1 studied the concave majorant process of a brownian motion b t, t. Abstractwe study the positive minorant property for norms on spaces of matrices. Get a printable copy pdf file of the complete article 477k, or click on a page image below to. Infima of families of superharmonic functions springerlink. We show that the difference of majorant and minorant.
Similar examples could be constructed in which 3 is replaced by any p 2 not equal to an even integer. On matrix majorants and mlnorants, with applications to. Telecharger majorant minorant borne sup borne inf borne. 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. Local convergence of newtons method under majorant.
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