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SUMMARY This is a survey paper on the recent development of the spectral theory of nonnegative tensors and its applications. After a brief review of the basic definitions on tensors, the H-eigenvalue problem and the Z-eigenvalue problem for tensors are studied separately. To the H-eigenvalue problem for nonnegative tensors, the whole Perron-Frobenius theory for nonnegative matrices is completely extended, while to the Z-eigenvalue problem, there are many distinctions and are studied carefully in details. Numerical methods are also discussed. Three kinds of applications are studied: higher order Markov chains, spectral theory of hypergraphs, and the quantum entanglement. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Summary: In this paper, we propose a new method for modelling precipitation in Sweden. We consider a chain dependent stochastic model that consists of a component that models the probability of occurrence of precipitation at a weather station and a component that models the amount of precipitation at the station when precipitation does occur. For the first component, we show that for most of the weather stations in Sweden a Markov chain of an order higher than one is required. For the second component, which is a Gaussian process with transformed marginals, we use a composite of the empirical distribution of the amount of precipitation below a given threshold and the generalized Pareto distribution for the excesses in the amount of precipitation above the given threshold. The derived models are then used to compute different weather indices. The distribution of the modelled indices and the empirical ones show good agreement, which supports the choice of the model. [Copyright &y& Elsevier]