We introduce and study very general stochastic positive linear operators induced by general positive linear operators that are acting on continuous functions. These are acting on the space of real differentiable stochastic processes. Under some very mild, general and natural assumptions on the stochastic processes we produce related stochastic Shisha–Mond type inequalities of L-type 1 ≤ q < ∞ a...

In this paper, an L°°(Ll )-error estimate for a class of finite volume methods for the approximation of scalar multidimensional conservation laws is obtained. These methods can be formally high-order accurate and are defined on general triangulations. The error is proven to be of order ft'/4 , where h represents the "size" of the mesh, via an extension of Kuznetsov approximation theory for whic...

We examine solutions u = PI f to ∆u − V u = 0 on a Lipschitz domain Ω in a compact Riemannian manifold M , satisfying u = f on ∂Ω, with particular attention to ranges of (s, p) for which one has Besov-to-L-Sobolev space results of the form PI : B s (∂Ω) −→ Lps+1/p(Ω), and variants, when the metric tensor on M has limited regularity, described by a Hölder or a Dini-type modulus of continuity. We...

A nonparametric adaptation theory is developed for the construction of confidence intervals for linear functionals. A between class modulus of continuity captures the expected length of adaptive confidence intervals. Sharp lower bounds are given for the expected length and an ordered modulus of continuity is used to construct adaptive confidence procedures which are within a constant factor of ...

*Correspondence: [email protected] 2Department of Mathematics, Gauhati University, Guwahati, India Full list of author information is available at the end of the article Abstract The notion of statistical weighted B-summability was introduced very recently (Kadak et al. in Appl. Math. Comput. 302:80–96, 2017). In the paper, we study the concept of statistical deferred weighted B-summ...

Following D. B. H. Cline [Cl], we study the connections between the behavior of the spherical mean of an L modulus of continuity corresponding to the finite difference of an arbitrary order m > 0 of a function f ∈ L(R), 1 ≤ p ≤ ∞, d ∈ N, and the average decay of the Fourier transform f̂ . We obtain an estimate which refines one result from [Cl] for 1 ≤ p ≤ 2. Our main interest is in two-sided es...

We consider a compact set K in the form of a sequence of segments. By means of nearly Chebyshev polynomials for K, the modulus of continuity of the Green functions gC\K is estimated. Markov’s constants of the corresponding set are evaluated.

A detailed analysis of minimax estimates of arbitrary linear functionals based on infinite dimensional Gaussian models has been provided by Donoho and Liu. In particular it has been shown that if the parameter space is convex then linear estimates can always be found which have maximum mean squared error within a small constant multiple of the minimax value. These linear estimates do however ha...

We consider uniqueness theorems in classical analysis having the form (+) ∀u ∈ U, v1, v2 ∈ Vu ( G(u, v1) = 0 = G(u, v2) → v1 = v2 ) , where U, V are complete separable metric spaces, Vu is compact in V and G : U × V → IR is a constructive function. If (+) is proved by arithmetical means from analytical assumptions (++) ∀x ∈ X∃y ∈ Yx∀z ∈ Z ( F (x, y, z) = 0 ) only (where X, Y, Z are complete sep...

In this article we study the exponential behavior of the continuous stochastic Anderson model, i.e. the solution of the stochastic partial differential equation u(t, x) = 1+ ∫ t 0 κ∆xu (s, x) ds+ ∫ t 0 W (ds, x)u (s, x), when the spatial parameter x is continuous, specifically x ∈ R, and W is a Gaussian field on R+ × R that is Brownian in time, but whose spatial distribution is widely unrestric...