相关论文: Asymptotics of generalized P\'olya urns with non-l…

Cumulative advantage (CA) refers to the notion that accumulated resources foster the accumulation of further resources in competitions, a phenomenon that has been empirically observed in various contexts. The oldest and arguably simplest…

We propose a variant model of P{\'o}lya urn process, where the dynamics consist of two competing elements namely, suppression of growth and enhancement of dormant character. Here the level of such features are controlled by an internal…

Regression models for continuous outcomes often require a transformation of the outcome, which the user either specify {\it a priori} or estimate from a parametric family. Cumulative probability models (CPMs) nonparametrically estimate the…

Non-standard distributional approximations have received considerable attention in recent years. They often provide more accurate approximations in small samples, and theoretical improvements in some cases. This paper shows that the…

We study self-organized models for information transmission and herd behavior in financial markets. Existing models are generalized to take into account the effect of size-dependent fragmentation and coagulation probabilities of groups of…

We consider P\'olya urns with infinitely many colours that are of a random walk type, in two related version. We show that the colour distribution a.s., after rescaling, converges to a normal distribution, assuming only second moments on…

Stochastic feedback systems give rise to a variety of notions of stability. The conditions for the stability of the median, mean, and variance stability conditions differ. These conditions can be stated explicitly for scalar discrete-time…

We consider a model of N two-colors urns in which the reinforcement of each urn depends also on the content of all the other urns. This interaction is of mean-field type and it is tuned by a parameter $\alpha$ in [0,1]; in particular, for…

We consider a version of the classical P\'olya urn scheme which incorporates innovations. The space $S$ of colors is an arbitrary measurable set. After each sampling of a ball in the urn, one returns $C$ balls of the same color and…

We define and prove limit results for a class of dominant P\'olya sequences, which are randomly reinforced urn processes with color-specific random weights and unbounded number of possible colors. Under fairly mild assumptions on the…

We propose a general notion of dissipativity with dynamic supply rates for nonlinear systems. This extends classical dissipativity with static supply rates and dynamic supply rates of miscellaneous quadratic forms. The main results of this…

In this paper, we consider a new type of urn scheme, where the selection probabilities are proportional to a weight function, which is linear but decreasing in the proportion of existing colours. We refer to it as the \emph{negatively…

We study asymptotic behavior of solutions of the first-order linear consensus model with delay and anticipation, which is a system of neutral delay differential equations. We consider both the transmission-type and reaction-type delay that…

A distributed average consensus algorithm in which every sensor transmits with bounded peak power is proposed. In the presence of communication noise, it is shown that the nodes reach consensus asymptotically to a finite random variable…

This paper studies whether solutions of a class of nonlinear feedback systems remain bounded over time. The systems we consider arise naturally in synthetic biology, where the antithetic feedback controller regulates a biological process…

For a general class of dynamical systems (of which the canonical continuous and uniform discrete versions are but special cases), we prove that there is a state feedback gain such that the resulting closed-loop system is uniformly…

Following Hales (2018), the evolution of P\'olya's urn may be interpreted as a walk, a P\'olya walk, on the integer lattice $\mathbb{N}^2$. We study the visibility properties of P\'olya's walk or, equivalently, the divisibility properties…

A competition process is a continuous time Markov chain that can be interpreted as a system of interacting birth-and-death processes, the components of which evolve subject to a competitive interaction. This paper is devoted to the study of…

We investigate consensus formation and flocking behavior in multi-agent systems subject to two distinct types of delays: a transmission delay accounting for information exchange between agents, and a reaction delay representing the…

We consider the problem of output feedback stabilization in linear systems when the measured outputs and control inputs are subject to event-triggered sampling and dynamic quantization. A new sampling algorithm is proposed for outputs which…