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Consider Z i  = ( X i , Y i ), i  ∈ ℤ N be an F×ℝ-valued measurable strictly stationary spatial process, where F is a semi-metric space. We study the spatial covariation between X i and Y i by using the local linear estimate of the functional spatial regression E[ Y i | X i ]. The main result of this work is the establishment of the almost complete convergence for the proposed estimator, under some general conditions. We illustrate our methodology by applying the estimator to climatological data.

We are interested in the problem of estimating a regression function φ observed with a correlated noise Y  =  φ ( X )+ U . Contrary to the usual regression model, U is not centered conditionaly on X but rather on an observed variable W . Hence this model turns to be a difficult inverse problem where the corresponding operator is unknown since it is related to the joint distribution of ( X,W ). We focus on the case where the eigenvalues of the corresponding operator are observed with small perturbations and, using a well adapted spectral cut-off estimation procedure, we build a data driven estimates and derive an oracle inequality.

We give a unified mathematical framework for reduced-form models for portfolio credit risk and identify properties which lead to positive dependence of default times. Dependence in the default hazard rates is modeled by common macroeconomic factors as well as by inter-obligor links. It is shown that popular models produce positive dependence between defaults in terms of association. Implications of these results are discussed, in particular when we turn to pricing of credit derivatives. In mathematical terms our paper contains results about association of a class of non-Markovian processes.

We consider the problem of maximizing the utility of consumption and terminal wealth in a geometric Ornstein–Uhlenbeck market. We calculate the optimal consumption and wealth processes for power, logarithmic and exponential utility as well as their behavior depending e.g. on subjective discounting or the time horizon. We also use a specific example to show the identity of the solutions calculated by the primal and the dual method.