This thesis concerns the theory of positive-definite completions and its mutually beneficial connections to the statistics of function-valued or continuously-indexed random processes, better known as functional data analysis. In particular, it dwells upon ...
The Byzantine consensus problem involves.. processes, out of which t < n could be faulty and behave arbitrarily. Three properties characterize consensus: (1) termination, requiring correct (nonfaulty) processes to eventually reach a decision, (2) agreement ...
We review the current state of statistical modeling of asymptotically independent data. Our discussion includes necessary and sufficient conditions for asymptotic independence, results on the asymptotic independence of statistics of interest, estimation an ...
We prove a version of Myers-Steenrod's theorem for Finsler manifolds under the minimal regularity hypothesis. In particular we show that an isometry between C-k,C-alpha-smooth (or partially smooth) Finsler metrics, with k + alpha > 0, k is an element of N ...
Given a sequence L & x2d9;epsilon of Levy noises, we derive necessary and sufficient conditions in terms of their variances sigma 2(epsilon) such that the solution to the stochastic heat equation with noise sigma(epsilon)-1L & x2d9;epsilon converges in law ...
