We construct a continuous distribution G such that the number of faces in the smallest concave majorant of the random walk with G-distributed summands will take on each natural number infinitely often with probability one. This investigation is motivated by the fact that the number of faces Fn of the concave majorant of the random walk at time n has the same distribution as the number of record...

Preferences and endowments. Consider a static endowment economy populated by a continuum of households. The households have identical preferences expressed by a strictly increasing strictly concave utility function U(c) over a single consumption good. The households have heterogeneous endowments y ∈ [0,∞) of this single consumption good distributed with density f(y) > 0 in the population. Let Y...

We study stochastic team problems with static information structure where we assume controllers have linear information and quadratic cost but allow the noise to be from a non-Gaussian class. When the noise is Gaussian, it is well known that these problems admit linear optimal controllers. We show that for such linear-quadratic static teams with any logconcave noise, if the length of the noise ...

We introduce the antipodal pairs property for probability measures on finite Boolean algebras and prove that conditional versions imply strong forms of log-concavity. We give several applications of this fact, including improvements of some results of Wagner [15]; a new proof of a theorem of Liggett [9] stating that ultra-log-concavity of sequences is preserved by convolutions; and some progres...

Given continuous functions M and N of two variables, it is shown that if in a continuous iteration semigroup with only (M,N)-convex or (M,N)-concave elements there are two (M,N)-affine elements, then M = N and every element of the semigroup is M -affine. Moreover, all functions in the semigroup either are M -convex or M -concave.

While attracting attention is one of the prime goals of content providers, the conversion of that attention into revenue is by no means obvious. Given that most users expect to consume web content for free, a provider with an established audience faces a dilemma. Since the introduction of advertisements or subscription fees will be construed by users as an inconvenience which may lead them to s...

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Based on empirical Levy-type concentration functions a new graphical representation of the ML-density estimator under order restrictions is given. This representation generalizes the well-known representation of the Grenander estimator of a monotone density as the slope of the least concave majorant of the empirical distribution function. From the given representation it follows that a density ...

The pulse inversion averaging (PIA) method is introduced to the shadowgraph imaging system to visualize the second-harmonic component of the ultrasonic field. The principle of the PIA method is summarized and the method is customized for observing an second-harmonic ultrasonic field. An experiment of a shadowgraph with PIA using a 1-MHz concave focused transducer is conducted to evaluate the sy...

In the paper we study closures of classes of log–concave measures under taking weak limits, linear transformations and tensor products. We consider what uniform measures on convex bodies can one obtain starting from some class K. In particular we prove that if one starts from one–dimensional log–concave measures, one obtains no non– trivial uniform mesures on convex bodies.