We consider a class of risk processes with delayed claims, and we provide ruin probability estimates under large claim assumptions

We present a mesoscopic model, based on the Boltzmann equation, for the interaction between a solid wall and a nonideal fluid. We present an analytic derivation of the contact angle in terms of the surface tension between the liquid-gas, the liquid-solid, and the gas-solid phases. We study the dependency of the contact angle on the two free parameters of the model, which determine the interaction between the fluid and the boundaries, i.e. the equivalent of the wall density and of the wall-fluid potential in molecular dynamics studies. We compare the analytical results obtained in the hydrodynamical limit for the density profile and for the surface tension expression with the numerical simulations. We compare also our two-phase approach with some exact results obtained by E. Lauga and H. Stone ?J. Fluid. Mech. 489, 55 ?2003?? and J. Philip ?Z. Angew. Math. Phys. 23, 960 ?1972?? for a pure hydrodynamical incompressible fluid based on Navier-Stokes equations with boundary conditions made up of alternating slip and no-slip strips. Finally, we show how to overcome some theoretical limitations connected with the discretized Boltzmann scheme proposed by X. Shan and H. Chen ?Phys. Rev. E 49, 2941 ?1994?? and we discuss the equivalence between the surface tension defined in terms of the mechanical equilibrium and in terms of the Maxwell construction.

The regularized linear wavelet estimator has been recently proposed as an alternative to the spline smoothing estimator, one of the most used linear estimator for the standard nonparametric regression problem. It has been demonstrated that the regularized linear wavelet estimator attains the optimal rate of convergence in the mean integrated squared error sense and compares favorably with the smoothing spline estimator in finite-sample situations, especially for less smooth response functions. We investigate further this estimator, extending Bayesian aspects of smoothing splines considered earlier in the literature. We first consider a Bayesian formalism in the wavelet domain that gives rise to the regularized linear wavelet estimator obtained in the standard nonparametric regression setting. We then use the posterior distribution to construct pointwise Bayesian credible intervals for the resulting regularized linear wavelet function estimate. Simulation results show that the wavelet-based pointwise Bayesian credible intervals have good empirical coverage rates for standard nominal coverage probabilities and compare favorably with the corresponding intervals obtained by smoothing splines, especially for less smooth response functions. Moreover, their construction algorithm is of order O(n) and it is easily implemented.

We consider a Bayesian approach to multiple hypothesis testing. A hierarchical prior model is based on imposing a prior distribution $\pi(k)$ on the number of hypotheses arising from alternatives (false nulls). We then apply the maximum a posteriori (MAP) rule to find the most likely configuration of null and alternative hypotheses. The resulting MAP procedure and its closely related step-up and step-down versions compare ordered Bayes factors of individual hypotheses with a sequence of critical values depending on the prior. We discuss the relations between the proposed MAP procedure and the existing frequentist and Bayesian counterparts. A more detailed analysis is given for the normal data, where we show, in particular, that choosing a specific $\pi(k)$, the MAP procedure can mimic several known familywise error (FWE) and false discovery rate (FDR) controlling procedures. The performance of MAP procedures is illustrated on a simulated example.

We consider the testing problem in the mixed-effects functional analysis of variance models. We develop asymptotically optimal (minimax) testing procedures for testing the significance of functional global trend and the functional fixed effects based on the empirical wavelet coefficients of the data. Wavelet decompositions allow one to characterize various types of assumed smoothness conditions on the response function under the nonparametric alternatives. The distribution of the functional random-effects component is defined in the wavelet domain and captures the sparseness of wavelet representation for a wide variety of functions. The simulation study presented in the paper demonstrates the finite sample properties of the proposed testing procedures. We also applied them to the real data from the physiological experiments.

In recent years a number of variational models related to reconstruction problems in computer vision have been proposed.

We study the convergence and decay rate to equilibrium of bounded solutions of the quasilinear parabolic equation ut - div a(x , ? u) + f (x , u) = 0 on a bounded domain, subject to Dirichlet boundary and to initial conditions. The data are supposed to satisfy suitable regularity and growth conditions. Our approach to the convergence result and decay estimate is based on the ?ojasiewicz-Simon gradient inequality which in the case of the semilinear heat equation is known to give optimal decay estimates. The abstract results and their applications are discussed also in the framework of Orlicz-Sobolev spaces.

We prove a semi-continuity theorem for an integral functional made up by a polyconvex energy and a surface term. Our result extends a well-known result by Ball to the BV framework.

We show the Gamma-convergence of a family of discrete functionals to the Mumford and Shah image segmentation functional. The functionals of the family are constructed by modifying the elliptic approximating functionals proposed by Ambrosio and Tortorelli. The quadratic term of the energy related to the edges of the segmentation is replaced by a nonconvex functional.

The objective of this paper is the derivation and the analysis of a simple explicit numerical scheme for general one-dimensional filtration equations. It is based on an alternative formulation of the problem using the pseudoinverse of the density's repartition function. In particular, the numerical approximations can be proven to satisfy a contraction property for a Wasserstein metric. Various numerical results illustrate the ability of this numerical process to capture the time-asymptotic decay towards self-similar solutions even for fast-diffusion equations.

Abstract. One-dimensional electronic conduction is investigated in a special case usually referred to as the harmonic crystal, meaning essentially that atoms are assumed to move like coupled harmonic oscillators within the Born–Oppenheimer approximation. We recall their dispersion relation and derive a WKB system approximately satisfied by any electron's wavefunction inside a given energy band. This is then numerically solved according to the method of K-branch solutions. Numerical results are presented in the case where atoms move with one- or two-modes vibrations; finally, we include the case where the Poisson self-interaction potential also influences the electrons' dynamics.

An extended FitzHugh-Nagumo model coupled with dynamical heat transfer in tissue, as described by a bioheat equation, is derived and confronted with experiments. The main outcome of this analysis is that traveling pulses and spiral waves of electric activity produce temperature variations on the order of tens of 0°C. In particular, the model predicts that a spiral wave’s tip, heating the surrounding medium as a consequence of the Joule effect, leads to characteristic hot spots. This process could possibly be used to have a direct visualization of the tip’s position by using thermal detectors.

The definition of relative accelerations and strains among a set of comoving particles is studied in connection with the geometric properties of the frame adapted to a \lq\lq fiducial observer." We find that a relativistically complete and correct definition of strains must take into account the transport law of the chosen spatial triad along the observer's congruence. We use special congruences of (accelerated) test particles in some familiar spacetimes to elucidate such a point. The celebrated idea of Szekeres' compass of inertia, arising when studying geodesic deviation among a set of free-falling particles, is here generalized to the case of accelerated particles. In doing so we have naturally contributed to the theory of relativistic gravity gradiometer. Moreover, our analysis was made in an observer-dependent form, a fact that would be very useful when thinking about general relativistic tests on space stations orbiting compact objects like black holes and also in other interesting gravitational situations.

The accurate calibration of thousands of thermometers involves the optimzation of the experimental design to save time and costs. A modelling procedure is proposed for the construction of a suitable free-knots cubic spline model. An iterative algorithm is used and a minimum experimental design is identified.