Storage systems based on weak consistency provide better availability and lower latency than systems that use strong consistency, especially in geo-replicated settings. However, under weak consistency, it is harder to ensure the correctness of applications, as the execution of uncoordinated operations may lead to invalid states. In this paper we show how to modify an application to make it run ...

Morphological openings and closings can be viewed as consistent MAP estimators of smooth random binary image signals immersed in i.i.d. clutter, or suffering from i.i.d. random dropouts. We revisit this viewpoint under much more general assumptions and show that, quite surprisingly, the above interpretation is still valid.

We consider the case 1 interval censorship model in which the survival time has an arbitrary distribution function F 0 and the inspection time has a discrete distribution function G. In such a model one is only able to observe the inspection time and whether the value of the survival time lies before or after the inspection time. We prove the strong consistency of the generalized maximum likeli...

The Forward Search is a powerful general method for detecting anomalies in structured data, whose diagnostic power has been shown in many statistical contexts. However, despite the wealth of empirical evidence in favour of the method, only few theoretical properties have been established regarding the resulting estimators. We show that the Forward Search estimators are strongly consistent at th...

Abstract: Let {Xn, n=1} be a sequences of i.i.d. random variables with survival function 1 F(x) P[X x] = > . A wavelet linear survival function n F(x) based on X1, X2,..., Xn is introduced as an estimator for n F(x) . We establish that the Lp’-loss (2=r=p′= ∞) of the linear wavelet survival function estimator for a stochastic processes convergence at the rate rs 2 s 1 n (s s 1 /p 1 / p ) ′ − ′+...

We use Lax equations to define a scattering problem on an infinite elbow shaped line of the (x, t) plane. The evolution of scattering coefficients when the elbow is translated in the plane shows how convenient scannings may reconstruct the solution V (x, t) of the nonlinear equation associated to the Lax pair. It also helps us understanding why this can work only if strong consistency condition...

This paper presents a Bayesian nonparametric approach to the estimation of a system and its components’ survival functions arising from observing the failure of a series system or a competing-risks model. A Dirichlet multivariate process is used as a prior for the vector of the components’ random subsurvival function to derive the Bayes estimator of the survival function when the cause of failu...

Strong consistency and asymptotic normality of the Gaussian pseudo-maximum likelihood estimate of the parameters in a wide class of ARCH(∞) processes are established. The conditions are shown to hold in case of exponential and hyperbolic decay in the ARCH weights, though in the latter case a faster decay rate is required for the central limit theorem than for the law of large numbers. Particula...

Copulas are extensively used for dependence modeling. In many cases the data does not reveal how the dependence can be modeled using a particular parametric copula. Nonparametric copulas do not share this problem since they are entirely data based. This paper proposes nonparametric estimation of the density copula for α−mixing data using Bernstein polynomials. We study the asymptotic properties...

Parameter-dependent linear evolution equations with a fractional noise in the boundary conditions are studied. Ergodic-type theorems for stationary and non-stationary solutions are verified and used to prove the strong consistency of a suitably defined family of estimators.