This paper establishes the asymptotic normality of frequency polygons in the context of stationary strongly mixing random fields indexed by <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\mathbb {Z}^d$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msup> <mrow> <mi mathvariant="double-struck">Z</mi> </mrow> <mi>d</mi> </msup> </math> </EquationSource> </InlineEquation>. Our method allows us to consider only minimal conditions on the width bins and provides a simple criterion on the mixing...</equationsource></equationsource></inlineequation>

We consider the optimization problem of a campaign trying to win an election when facing aggregate uncertainty, where agentsʼ voting probabilities are uncertain. Even a small amount of uncertainty will in a large electorate eliminate many of counterintuitive results that arise when voting...

Random walks in random scenery are processes defined by Zn:=∑k=1nωSk where S:=(Sk,k≥0) is a random walk evolving in Zd and ω:=(ωx,x∈Zd) is a sequence of i.i.d. real random variables. Under suitable assumptions on the random walk S and the random scenery ω, almost surely with respect to...

We consider renewal shot noise processes with response functions which are eventually nondecreasing and regularly varying at infinity. We prove weak convergence of renewal shot noise processes, properly normalized and centered, in the space D[0,∞) under the J1 or M1 topology. The limiting...

Consider an i.i.d. random field {Xk:k∈Z+d}, together with a sequence of unboundedly increasing nested sets Sj=⋃k=1jHk,j≥1, where the sets Hj are disjoint. The canonical example consists of the hyperbolas Hj={k∈Z+d:|k|=j}. We are interested in the number of “hyperbolas” Hj that...

We study subsampling estimators for the limit variance σ2=V ar(X1)+2∑k=2∞Cov(X1,Xk) of partial sums of a stationary stochastic process (Xk)k≥1. We establish L2-consistency of a non-overlapping block resampling method. Our results apply to processes that can be represented as functionals...

The Birnbaum–Saunders distribution is based on the asymptotic normality of a sum of random variables. We propose a new version of this distribution assuming that the number of terms of such a sum depends on a non-homogeneous Poisson process. The classical Birnbaum–Saunders distribution is...