Recently, the martingale property and conditional expectations w.r.t. the natural filtration of Brownian motion for (generalized) processes have been studied by [9], [3], [6], and [8] in the context of white noise analysis. For regular processes these characterizations are an immediate consequence of the chaos expansion w.r.t. multiple stochastic integrals. They have turned out to be useful for...

For a function f ∈ L2,γ (ℝ2), the q-averaging of generalized m-order modulus continuity Ωm,γ (f) with weight φ, i.e., value

In this paper we consider a φ-irreducible continuous parameter Markov process Φ whose state space is a general topological space. The recurrence and Harris recurrence structure of Φ is developed in terms of generalized forms of resolvent chains, where we allow statemodulated resolvents and embedded chains with arbitrary sampling distributions. We show that the recurrence behavior of such genera...

Charles[1] proved the convergence of Picard-type iterative for generalized Φ− accretive non-self maps in a real uniformly smooth Banach space. Based on theorems zeros strongly quasi- and fixed points hemi-contractions, we extend results to Ishikawa iteration process with er- rors hemi-contractive .

We develop a renormalization-group formalism for non-renormalizable theories and apply it to Einstein gravity theory coupled to a scalar field with the Lagrangian L = √ g [RU(φ) − 1 2 G(φ) gμν ∂μφ∂νφ − V (φ)], where U(φ), G(φ) and V (φ) are arbitrary functions of the scalar field. We calculate the one-loop counterterms of this theory and obtain a system of renormalization-group equations in par...

We essentially extend and improve the classical result of G. H. Hardy J. E. Littlewood on strong summability Fourier series. will present an estimation generalized mean (H, Φ) as approximation version Totik type generaliza- tion Hardy, Littlewood, in case integrable functions from LΨ. As a measure such we use function constructed by Ψ com- plementary to Φ base definition LΨ points. Some corolla...

A generalized two-dimensional word is a function on Z with a finite number of values. The main problem we are interested in is periodicity of twodimensional words satisfying some local conditions. Let A be a matrix of order n. The function φ : Z → R is a generalized centered function of radius r with the matrix A if ∑ y ∈ Z2 : 0 < |y − x| ≤ r φ(y) = φ(x)A for every x ∈ Z, where for x = (x1, x2)...