In this paper, we prove uniform Morrey-Campanato type estimates for this equation, using a multiplier method borrowed from [9]. These bounds encode in the optimal way the decay: |u(x)| ∼ 1/|x| d−1 2 at infinity of the solution u. They imply weighted L-estimates for the solution u. We also prove a uniform L-estimate without weight for the trace of the solution on the interface, which states that...

3.1 Maximum likelihood estimates — in exponential families. Let (X, B) be a measurable space and {P θ , θ ∈ Θ} a measurable family of laws on (X, B), dominated by a σ-finite measure v. Let f (θ, x) be a jointly measurable version of the density (dP θ /dv)(x) by Theorem 1.3.3. For each x ∈ X, a maximum likelihood estimate (MLE) of θ is any θ ˆ = θ ˆ (x) such that f (ˆ θ, x) = sup{f (φ, x) : φ ∈ ...

‎Semidiscrete finite element approximation of a hyperbolic type‎ ‎integro-differential equation is studied. The model problem is‎ ‎treated as the wave equation which is perturbed with a memory term.‎ ‎Stability estimates are obtained for a slightly more general problem.‎ ‎These, based on energy method, are used to prove optimal order‎ ‎a priori error estimates.‎

We suggest an iterative approach to computing K-step maximum likelihood estimates (MLE) of the parametric components in semiparametric models based on their profile likelihoods. The higher order convergence rate of K-step MLE mainly depends on the precision of its initial estimate and the convergence rate of the nuisance functional parameter in the semiparametric model. Moreover, we can show th...

Point estimation for the selected treatment in a two-stage drop-the-loser trial is not straightforward because a substantial bias can be induced in the standard maximum likelihood estimate (MLE) through the first stage selection process. Research has generally focused on alternative estimation strategies that apply a bias correction to the MLE; however, such estimators can have a large mean squ...

The classical Schauder type results on C-regularity of solutions are exposed for linear second order elliptic equations with Hölder coefficients. Our approach is based on equivalent seminorms in Hölder spaces C, which are similar to seminorms introduced by S. Campanato [1]. Under this approach, the C-estimates for solutions are derived from the maximum principle and the interior smoothness of h...

The SGI POWER CHALLENGEarray TM represents a hierarchical supercomputer because it combines distributed and shared memory technology. We present two projects, Europort and GeneCrunch, that took advantage of such a configuration. In Europort we performed scalability demonstrations up to 64 processors with applications relevant to the chemical and pharmaceutical industries. GeneCrunch, a project ...

This paper presents a novel method that effectively combines both control variates and importance sampling in a sequential Monte Carlo context. The radiance estimates computed during the rendering process are cached in a 5D adaptive hierarchical structure that defines dynamic predicate functions for both variance reduction techniques and guarantees well-behaved PDFs, yielding continually increa...