The paper studies properties of continuous time processes in pathwise deterministic setting with spectrum degeneracy at a single point where their Fourier transforms vanish. It appears that these processes are predictable is some weak sense, meaning that convolution integrals over future time can be approximated by integrals over past time. In particular, this means that the processes with this...

Probability theory is an important tool of modeling randomness in a practical problem. But besides randomness, in the real world, there exists other kind of uncertainties such as impreciseness or vagueness. Set-valued functions are employed to model the impreciseness in applied field such as in Economics, control theory (see for example [1]). Integrals of set-valued functions have been received...

The paper studies stochastic integration with respect to Gaussian processes and fields. It is more convenient to work with a field than a process: by definition, a field is a collection of stochastic integrals for a class of deterministic integrands. The problem is then to extend the definition to random integrands. An orthogonal decomposition of chaos space of the random field leads to two suc...

We study pathwise predictability of continuous time processes in deterministic setting, when the convolution integrals over future time can be approximated by integrals over past time. Uniform prediction in some weak sense with respect to certain classes of inputs is discussed. We found that all band-limited processes are predictable in this sense, as well as high-frequent processes with zero e...

The second Appell’s hypergeometric function F2(a, b, b ′, c, c′;x, y) has a Mellin convolution integral representation in the region (x + y) < 1 and a > 0. We apply a recently introduced asymptotic method for Mellin convolution integrals to derive three asymptotic expansions of F2(a, b, b ′, c, c′;x, y) in decreasing powers of x and y with x/y bounded. For certain values of the real parameters ...

Keywords: Filter Modular space (Modular) filter convergence Rate of convergence Sampling operator Integral operator Urysohn operator Mellin convolution operator a b s t r a c t We investigate the order of approximation of a real-valued function f by means of suitable families of sampling type operators, which include both discrete and integral ones. We give a unified approach, by means of which...

Considering the network structure is one of the new approaches in studying stochastic PERT networks (SPN). In this paper, planar networks are studied as a special class of networks. Two structural reducible mechanisms titled arc contraction and deletion are developed to convert any planar network to a series-parallel network structure.&#10In series-parallel SPN, the completion time distribution...

The Hartree-Fock eigenvalue problem governed by the 3D integro-differential operator is the basic model in ab initio electronic structure calculations. Several years ago the idea to solve the Hartree-Fock equation by fully 3D grid based numerical approach seemed to be a fantasy, and the tensor-structured methods did not exist. In fact, these methods evolved during the work on this challenging p...

We study pathwise predictability of continuous time processes in deterministic setting, when the convolution integrals over future time can be approximated by integrals over past time. Uniform prediction in some weak sense with respect to certain classes of inputs is discussed. We found that all band-limited processes are predictable in this sense, as well as high-frequent processes with zero e...