Related papers: Self-averaging sequences which fail to converge
We provide a general framework to study stochastic sequences related to individual learning in economics, learning automata in computer sciences, social learning in marketing, and other applications. More precisely, we study the asymptotic…
Linear nonautonomous/random parabolic partial differential equations are considered under the Dirichlet, Neumann or Robin boundary conditions, where both the zero order coefficients in the equation and the coefficients in the boundary…
We prove a central limit theorem for a sequence of random variables whose means are ambiguous and vary in an unstructured way. Their joint distribution is described by a set of measures. The limit is (not the normal distribution and is)…
Convergent sequences of real numbers play a fundamental role in many different problems in system theory, e.g., in Lyapunov stability analysis, as well as in optimization theory and computational game theory. In this survey, we provide an…
We study the group Russian roulette problem, also known as the shooting problem, defined as follows. We have $n$ armed people in a room. At each chime of a clock, everyone shoots a random other person. The persons shot fall dead and the…
We prove pointwise convergence, as $N\to \infty$, for the multiple ergodic averages $\frac{1}{N}\sum_{n=1}^N f(T^nx)\cdot g(S^{a_n}x)$, where $T$ and $S$ are commuting measure preserving transformations, and $a_n$ is a random version of the…
It is known that limit theorems for triangular arrays with identically distributed rows yields convergence of densities rather than just convergence in distribution. We show that this superconvergence result holds -- at least at points at…
This work unifies the analysis of various randomized methods for solving linear and nonlinear inverse problems by framing the problem in a stochastic optimization setting. By doing so, we show that many randomized methods are variants of a…
We revisit the classical problem of universal prediction of stochastic sequences with a finite time horizon $T$ known to the learner. The question we investigate is whether it is possible to derive vanishing regret bounds that hold with…
We consider first order expressible properties of random perfect graphs. That is, we pick a graph $G_n$ uniformly at random from all (labelled) perfect graphs on $n$ vertices and consider the probability that it satisfies some graph…
I discuss group averaging as a method for quantising constrained systems whose gauge group is a noncompact Lie group. Focussing on three case studies, I address the convergence of the averaging, possible indefiniteness of the prospective…
We find the asymptotic distribution of the sample autocovariances of long-memory processes in cases of finite and infinite fourth moment. Depending on the interplay of assumptions on moments and the intensity of dependence, there are three…
We consider an edge-weighted uniform random graph with a given degree sequence (Repeated Configuration Model) which is a useful approximation for many real-world networks. It has been observed that the vertices which are separated from the…
The "typical" asymptotic behavior of the weighted sums of independent, identically distibuted random vectors in k-dimensional space is considered. It is shown that under finitnes of fifth absolute moment of an individual term the rate of…
We review some aspects of the use of a technique known as group averaging, which provides a tool for the study of constrained systems. We focus our attention on the case where the gauge group is non-compact, and a `renormalized' group…
We derive theorems which outline explicit mechanisms by which anomalous scaling for the probability density function of the sum of many correlated random variables asymptotically prevails. The results characterize general anomalous scaling…
We consider a family of multivariate autoregressive stochastic sequences that restart when hit a neighbourhood of the origin, and study their distributional limits when the autoregressive coefficient tends to one, the noise scaling…
The self-similar analysis of time series is generalized by introducing the notion of scenario probabilities. This makes it possible to give a complete statistical description for the forecast spectrum by defining the average forecast as a…
The incompressible limit of nonlinear diffusion equations of porous medium type has attracted a lot of attention in recent years, due to its ability to link the weak formulation of cell-population models to free boundary problems of…
A class of random recursive sequences (Y_n) with slowly varying variances as arising for parameters of random trees or recursive algorithms leads after normalizations to degenerate limit equations of the form X\stackrel{L}{=}X. For…