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作者：Bertini, L; Giacomin, G
作者单位：Sapienza University Rome; University of Zurich
摘要：We consider the stochastic heat equation in one space dimension and compute - for a particular choice of the initial datum - the exact long time asymptotic. In the Carmona-Molchanov approach to intermittence in non stationary random media this corresponds to the identification of the sample Lyapunov exponent, Equivalently, by interpreting the solution as the partition function of a directed polymer in a random environment, we obtain a weak law of large numbers for the quenched free energy. The...
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作者：Anshelevich, M
作者单位：University of California System; University of California Berkeley
摘要：We interpret the Central Limit Theorem as a fixed point theorem for a certain operator, and consider the problem of linearizing this operator. In classical as well as in free probability theory [VDN92], we consider two methods giving such a linearization, and interpret the result as a weak form of the CLT. In the classical case the analysis involves dilation operators; in the free case more general composition operators appear. Mathematical Subject Classification (1991): Primary 46L50; Seconda...
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作者：Gentz, B; Löwe, M
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Bielefeld
摘要：We investigate the limiting fluctuations of the order parameter in the Hopfield model of spin glasses and neural networks with finitely many patterns at the critical temperature 1/beta(c), = 1, At the critical temperature, the measure-valued random variables given by the distribution of the appropriately scaled order parameter under the Gibbs measure converge weakly towards a random measure which is non-Gaussian in the sense that it is not given by a Dirac measure concentrated in a Gaussian di...
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作者：Colubi, A; López-Díaz, M; Domínguez-Menchero, JS; Gil, MA
作者单位：University of Oviedo
摘要：Strong laws of large numbers have been stated in the literature for measurable functions taking on values on different spaces. In this paper, a strong law of large numbers which generalizes some previous ones (like those for real-valued random variables and compact random sets) is established. This law is an example of a strong law of large numbers for Borel measurable nonseparably valued elements of a metric space.
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作者：Barron, A; Birgé, L; Massart, P
作者单位：Yale University; Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay
摘要：Performance bounds for criteria for model selection are developed using recent theory for sieves. The model selection criteria are based on an empirical loss or contrast function with an added penalty term motivated by empirical process theory and roughly proportional to the number of parameters needed to describe the model divided by the number of observations. Most of our examples involve density or regression estimation settings and we focus on the problem of estimating the unknown density ...
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作者：Fontes, LRG; Isopi, M; Newman, CM
作者单位：Universidade de Sao Paulo; Sapienza University Rome; New York University
摘要：Stochastic Ising and voter models on Z(d) are natural examples of Markov processes with compact state spaces. When the initial state is chosen uniformly at random, can it happen that the distribution at time t has multiple (subsequence) limits as t --> infinity? Yes for the d = 1 Voter Model with Random Rates (VMRR)- which is the same as a d = 1 rate-disordered stochastic Ising model at zero temperature - if the disorder distribution is heavy-tailed. No (at least in a weak sense) for the VMRR ...
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作者：Chow, PL; Ibragimov, IA; Khasminskii, RZ
作者单位：Wayne State University; Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences; St. Petersburg Department of the Steklov Mathematical Institute of the Russian Academy of Sciences
摘要：For linear partial differential equations, some inverse source problems are treated statistically based on nonparametric estimation ideas. By observing the solution in a small Gaussian white noise, the kernel type of estimators is used to estimate the unknown source function and its partial derivatives.. It is proved that such estimators are consistent as the noise intensity tends to zero. Depending on the principal part of the differential operator, the optimal asymptotic rate of convergence ...
