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We study four discrete time stochastic systems on $bbN$ modeling processes of rumour spreading. The involved individuals can either have an active or a passive role, speaking up or asking for the rumour. The appetite in spreading or hearing the rumour is represented by a set of random variables whose distributions may depend on the individuals. Our goal is to understand - based on those random variables distribution - whether the probability of having an infinite set of individuals knowing the rumour is positive or not.
The aim of this paper is to study rumor processes in random environment. In a rumor process a signal starts from the stations of a fixed vertex (the root) and travels on a graph from vertex to vertex. We consider two rumor processes. In the firework
We consider the Maki-Thompson model for the stochastic propagation of a rumour within a population. We extend the original hypothesis of homogenously mixed population by allowing for a small-world network embedding the model. This structure is realiz
We prove several results concerning classifications, based on successive observations $(X_1,..., X_n)$ of an unknown stationary and ergodic process, for membership in a given class of processes, such as the class of all finite order Markov chains.
In this paper, we study the compressibility of random processes and fields, called generalized Levy processes, that are solutions of stochastic differential equations driven by $d$-dimensional periodic Levy white noises. Our results are based on the
We consider a new family of $R^d$-valued L{e}vy processes that we call Lamperti stable. One of the advantages of this class is that the law of many related functionals can be computed explicitely (see for instance cite{cc}, cite{ckp}, cite{kp} and ci