Related papers: On a class of space-time intrinsic random function…
The self-similarity in space and time (hereafter self-similarity), either deterministic or statistical, is characterized by similarity exponents and a function of scaled variable, called the scaling function. In the present paper, we…
In this paper we describe a theory of a cumulative distribution function on a space with an order from a probability measure defined in this space. This distribution function plays a similar role to that played in the classical case.…
From the integration of non-symmetrical hyperboles, a one-parameter generalization of the logarithmic function is obtained. Inverting this function, one obtains the generalized exponential function. We show that functions characterizing…
A new definition of coarse-grained quantities describing the dust flow in General Relativity is proposed. It assigns the coarse--grained expansion, shear and vorticity to finite-size comoving domains of fluid in a covariant,…
Computer simulations of first-order relaxation processes show that the spatial configurations of the system acquire an invariant shape once the stationary regime is attained. Inspired by them we find that, in any first-order relaxation…
The concept of an objective spatial direction in special relativity is investigated and theories assuming light-speed isotropy while accepting the existence of a privileged spatial direction are classified. A natural generalization of the…
Sampling theory in spaces other than the space of band-limited functions has recently received considerable attention. This is in part because the band-limitedness assumption is not very realistic in many applications. In addition,…
We study the spectral properties of the transfer matrix for a gonihedric random surface model on a three-dimensional lattice. The transfer matrix is indexed by generalized loops in a natural fashion and is invariant under a group of motions…
In this paper we consider asymptotic expansions for a class of sequences of symmetric functions of many variables. Applications to classical and free probability theory are discussed.
This work is a continuation of [7]. We consider a continuous-time birth-and-death process in which the transition rates have an asymptotical power-law dependence upon the position of the process. We establish rough exponential asymptotic…
Nonstationary Gaussian processes (GPs) are essential for modeling complex, locally heterogeneous spatial data. A common modeling approach is the spatial deformation method that warps the domain to recover isotropy. However, this static…
It has long been agreed by academics that the inversion method is the method of choice for generating random variates, given the availability of the quantile function. However for several probability distributions arising in practice a…
Spacetime must be foliable by spacelike surfaces for the quantum mechanics of matter fields to be formulated in terms of a unitarily evolving state vector defined on spacelike surfaces. When a spacetime cannot be foliated by spacelike…
In [20], we derived representation formulae for spatially periodic solutions to the generalized, inviscid Proudman-Johnson equation and studied their regularity for several classes of initial data. The purpose of this paper is to extend…
To know the statistical distribution of a variable is an important problem in management of resources. Distributions of the power law type are observed in many real systems. However power law distributions have an infinite variance and thus…
We study the asymptotic joint distribution of sample space--time covariance estimators of strictly stationary random fields. We do this without any marginal or joint distributional assumptions other than mild moment and mixing conditions.…
We prove a uniform functional law of the logarithm for the local empirical process. To accomplish this we combine techniques from classical and abstract empirical process theory, Gaussian distributional approximation and probability on…
Scattering from a non-smooth random field on the time domain is studied for plane waves that propagate simultaneously through the potential in variable angles. We first derive sufficient conditions for stochastic moments of the field to be…
Standard geostatistical models assume second order stationarity of the underlying Random Function. In some instances, there is little reason to expect the spatial dependence structure to be stationary over the whole region of interest. In…
As an extension of isotropic Gaussian random fields and Q-Wiener processes on d-dimensional spheres, isotropic Q-fractional Brownian motion is introduced and sample H\"older regularity in space-time is shown depending on the regularity of…