Quasi-stationary distributions as centrality measures of reducible graphs

In contrast, we will explain how the limiting distribution of the process conditioned to not being absorbed when it is observed can explain some complex behavior, as the

The rate of extinction θ(α) is the highest in this case, equal to 0.100. In fact, the process reaches the upper bound 100 very rarely, so that the behavior of the process is

Indeed, the estimate of this probability results from Chebychev inequality and variance estimates in which the process is started in n.. What the symbol precisely means is

The purpose of this paper is to present a probabilistic proof of the well-known result stating that the time needed by a continuous-time finite birth and death process for going

In the present paper we consider a general Markovian model for a metastable dynamics and we show how, under mild hypotheses, “soft measures and capacities” associated with a covering

The last reason why we introduced this toy model that combines two and three-dimensional graphs is that it illustrates some limits of our result: while using the three-dimensional

Keywords: Absorbing finite Markov process, quasi-stationary measure, Doob transform, quantitative bounds on convergence, spectral gap, logarithmic Sobolev inequality, finite birth

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