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In this article, we establish novel decompositions of Gaussian fields taking values in suitable spaces of generalized functions, and then use these decompositions to prove results about Gaussian multiplicative chaos. We prove two decomposition theorems. Th ...
We derive a covariance formula for the class of 'topological events' of smooth Gaussian fields on manifolds; these are events that depend only on the topology of the level sets of the field, for example, (i) crossing events for level or excursion sets, (ii ...
We consider the problem of estimating the slope function in a functional regression with a scalar response and a functional covariate. This central problem of functional data analysis is well known to be ill-posed, thus requiring a regularised estimation p ...
This paper deals with the resolution of inverse problems in a periodic setting or, in other terms, the reconstruction of periodic continuous-domain signals from their noisy measurements. We focus on two reconstruction paradigms: variational and statistical ...
This thesis addresses statistical inference for the resolution of inverse problems. Our work is motivated by the recent trend whereby classical linear methods are being replaced by nonlinear alternatives that rely on the sparsity of naturally occurring sig ...
Building simulation requires a large number of uncertain inputs and parameters. These include quantities that may be known with reasonable confidence, like the thermal properties of materials and building dimensions, but also inputs whose correct values ca ...
Real-life acquisition systems are fundamentally limited in their ability to reproduce point sources. For example, a point source object, a star say, observed with an optical telescope is blurred by the imperfect lenses composing the system. Mathematically, ...
In this paper we consider the problem of navigating emergency rescuers in buildings. The objective of the rescuer is to reach several critical regions in a building endangered by a spreading hazard and leave safely. We consider stochastic finite state mode ...
Polarimetric incoherent target decomposition aims at accessing physical parameters of illuminated scatters through the analysis of the target coherence or covariance matrix. In this framework, independent component analysis (ICA) was recently proposed as a ...
Institute of Electrical and Electronics Engineers2016
Traditional approaches to analysing functional data typically follow a two-step procedure, consisting in first smoothing and then carrying out a functional principal component analysis. The idea underlying this procedure is that functional data are well ap ...
