相关论文: A large deviations principle for the Maki-Thompson…

The continuous time Markov process considered in this paper belongs to a class of population models with linear growth and catastrophes. There, the catastrophes happen at the arrival times of a Poisson process, and at each catastrophe time,…

Demographic noise causes unlimited population growth in a broad class of models which, without noise, would predict a stable finite population. We study this effect on the example of a stochastic birth-death model which includes…

We develop stochastic variational inference, a scalable algorithm for approximating posterior distributions. We develop this technique for a large class of probabilistic models and we demonstrate it with two probabilistic topic models,…

We consider a two-dimensional time-inhomogeneous birth-death process to model the time-evolution of fake news in a population. The two components of the process represent, respectively, (i) the number of individuals (say spreaders) who know…

Large deviations for sums of i.i.d.\ random variables with stretched-exponential tails (also called Weibull or semi-exponential tails) have been well understood since the 60's, going back to Nagaev's seminal work. Many extensions in the…

Even in large systems, the effect of noise arising from when populations are initially small can persist to be measurable on the macroscale. A deterministic approximation to a stochastic model will fail to capture this effect, but it can be…

We study a variety of stochastic contact processes -- directly related to models of rumor and disease spreading -- from the viewpoint of their constants of motion, either exact or approximated. Much as in deterministic systems, constants of…

We propose a model for diffusion of two opposite opinions. Here, the decision to be taken by each individual is a random variable which depends on the tendency of the population, as well on its own trend characteristic. The influence of the…

We studied the mutual information between a stimulus and a large system consisting of stochastic, statistically independent elements that respond to a stimulus. The Mutual Information (MI) of the system saturates exponentially with system…

A key feature of a sequential study is that the actual sample size is a random variable that typically depends on the outcomes collected. While hypothesis testing theory for sequential designs is well established, parameter and precision…

We propose a model of rumor spreading in which susceptible, but skeptically oriented individuals may oppose the rumor. Resistance may be implemented either by skeptical activists trying to convince spreaders to stop their activity, becoming…

We consider a two-dimensional Hamiltonian system perturbed by a small diffusion term, whose coefficient is state-dependent and non-degenerate. As a result, the process consists of the fast motion along the level curves and slow motion…

We analyze a model designed to describe the spread and accumulation of opinions in a population. Inspired by the social contagion paradigm, our model is built on the classical SIR model of Kermack and McKendrick and consists in a system of…

The theory of large deviations deals with the probabilities of rare events (or fluctuations) that are exponentially small as a function of some parameter, e.g., the number of random components of a system, the time over which a stochastic…

This work continues the analysis of large deviations for randomly connected neural networks models of the brain. The originality of the model relies on the fact that the directed impact of one particle onto another depends on the state of…

In the consensus model with bounded confidence, studied by Deffuant et al. (2000), two randomly selected people who differ not too much in their opinion both shift their opinions towards each other. Now we restrict this exchange of…

The recent astonishing wide adhesion of french people to the rumor claiming `No plane did crash on the Pentagon on September the 11", is given a generic explanation in terms of a model of minority opinion spreading. Using a majority rule…

In this paper, we consider a kind of fully coupled slow fast motion, in which the slow variable satisfies the non Lipschitz condition. We prove that the stochastic flow of the slow variable exists and moreover, satisfies the large deviation…

A basic result of large deviations theory is Sanov's theorem, which states that the sequence of empirical measures of independent and identically distributed samples satisfies the large deviation principle with rate function given by…

We consider a family of continuous time symmetric random walks indexed by $k\in \mathbb{N}$, $\{X_k(t),\,t\geq 0\}$. For each $k\in \mathbb{N}$ the matching random walk take values in the finite set of states…