We consider stochastic sequences with periodically stationary generalized multiple increments of fractional order which combines cyclostationary, multi-seasonal, integrated and fractionally patterns. solve the filtering problem for linear functionals constructed from unobserved values a sequence this type based on observations noise sequence. For known matrices spectral densities, we obtain for...

The generalized Ball curves of Wang-Said type with a position parameter L not only unify the Wang-Ball curves and the Said-Ball curves, but also include several useful intermediate curves. This paper presents the dual functionals for the generalized Ball basis of Wang-Said type. The relevant basis transformation formulae are also worked out.

We study, from a classical point of view, how the truth of a statement about higher type functionals depends on the underlying model. The models considered are the classical set-theoretic finite type hierarchy and the constructively more meaningful models of Continuous Functionals, Hereditarily Effective Operations, as well as the closed term model of Gödel’s system T . The main results are cha...

In this work we deal with the stochastic homogenization of the initial boundary value problems of monotone type. The models of monotone type under consideration describe the deformation behaviour of inelastic materials with a microstructure which can be characterised by random measures. Based on the Fitzpatrick function concept we reduce the study of the asymptotic behaviour of monotone operato...

The Markov dilation of diffusion type processes is defined. Infinitesimal operators and stochastic differential equations for the obtained Markov processes are described. Some applications to the integral representation for functionals of diffusion type processes and to the construction of a replicating portfolio for a non-terminal contingent claim are considered.

The sequentially realizable functionals (denoted SR) is a class of “sequentially computable” higher-type functionals that are a strictly larger class than the PCF-computable functionals and that have very strong and natural mathematical properties. Longley [Lon98b] exhibited a functional H in SR with the property that if one adds H to the language PCF, then the resulting language, PCF+H, comput...

As first demonstrated by Chambolle and Lions the staircasing effect of the RudinOsher-Fatemi model can be reduced by using infimal convolutions of functionals containing higher order derivatives. In this paper, we examine a modification of such infimal convolutions in a general discrete setting. For the special case of finite difference matrices, we show the relation of our approach to the cont...

where Ψ and g are smooth functions, ξε t is a “fast” ergodic diffusion whileXε t is a “slow” diffusion type process, κ ∈ (0, 1/2). Under the assumption that g has zero barycenter with respect to the invariant distribution of the fast diffusion, we derive the main result from the moderate deviation principle for the family (ε−κ ∫ t 0 g(ξ ε s)ds)t≥0, ε ↘ 0 which has an independent interest as wel...

The main purpose of this paper is to establish with a constructive proof the following Hölder-type inequality: let A be a uniformly complete Φ-algebra, T be a positive linear functional, and p, q be rational numbers such that p−1 + q−1 = 1. Then the inequality T (|fg|) ≤ (T (|f |)) (T (|g|)) holds for all f, g ∈ A.

In Hilbert space L2(Rn), we prove the equivalence between the mod-ulus of smoothness and the K-functionals constructed by the Sobolev space cor-responding to the Fourier transform. For this purpose, Using a spherical meanoperator.