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We consider the one dimensional symmetric simple exclusion process with a slow bond. In this model, particles cross each bond at rate $N^2$, except one particular bond, the slow bond, where the rate is $N$. Above, $N$ is the scaling parameter. This model has been considered in the context of hydrodynamic limits, fluctuations and large deviations. We investigate moderate deviations from hydrodynamics and obtain a moderate deviation principle.
We consider the symmetric simple exclusion process with slow boundary first introduced in [Baldasso {it et al.}, Journal of Statistical Physics, 167(5), 2017]. We prove a law of large number for the empirical measure of the process under a longer tim
Consider the state space model (X_t,Y_t), where (X_t) is a Markov chain, and (Y_t) are the observations. In order to solve the so-called filtering problem, one has to compute L(X_t|Y_1,...,Y_t), the law of X_t given the observations (Y_1,...,Y_t). Th
The Poisson--Dirichlet distribution arises in many different areas. The parameter $theta$ in the distribution is the scaled mutation rate of a population in the context of population genetics. The limiting case of $theta$ approaching infinity is prac
We obtain sharp upper and lower bounds for the moderate deviations of the volume of the range of a random walk in dimension five and larger. Our results encompass two regimes: a Gaussian regime for small deviations, and a stretched exponential regime
Let $(xi_i,mathcal{F}_i)_{igeq1}$ be a sequence of martingale differences. Set $S_n=sum_{i=1}^nxi_i $ and $[ S]_n=sum_{i=1}^n xi_i^2.$ We prove a Cramer type moderate deviation expansion for $mathbf{P}(S_n/sqrt{[ S]_n} geq x)$ as $nto+infty.$ Our res