In part I, we address the issue of existence of solutions for Cauchy problems involving nonlinear hyperbolic equations for initial data in Sobolev spaces with scaling subcritical regularity. In particular, we analyse nonlinear estimates for null-forms in t ...
We consider the problem of estimating stochastic volatility for a class of second-order parabolic stochastic PDEs. Assuming that the solution is observed at high temporal frequency, we use limit theorems for multipower variations and related functionals to ...
This paper investigates the impact of Kron reduction on the performance of numerical methods applied to the analysis of unbalanced polyphase power systems. Specifically, this paper focuses on power-flow study, state estimation, and voltage stability assess ...
We consider a class of continuous-time branching processes called Markovian binary trees (MBTs), in which the individuals lifetime and reproduction epochs are modelled using a transient Markovian arrival process (TMAP). We develop methods for estimating th ...
PurposeThere is increasing interest in using fate and exposure models to spatially differentiate the impacts of chemical emissions. This work aims at exploring the operationalization in life cycle assessment (LCA) of spatially differentiated models for tox ...
In presence of sparse noise we propose kernel regression for predicting output vectors which are smooth over a given graph. Sparse noise models the training outputs being corrupted either with missing samples or large perturbations. The presence of sparse ...
A new numerical method based on numerical homogenization and model order reduction is introduced for the solution of multiscale inverse problems. We consider a class of elliptic problems with highly oscillatory tensors that varies on a microscopic scale. W ...
We investigate regularized algorithms combining with projection for least-squares regression problem over a Hilbert space, covering nonparametric regression over a reproducing kernel Hilbert space. We prove convergence results with respect to variants of n ...
In this paper, we study regression problems over a separable Hilbert space with the square loss, covering non-parametric regression over a reproducing kernel Hilbert space. We investigate a class of spectral/regularized algorithms, including ridge regressi ...
