In this paper, we prove that a fuzzy set–valued Brownian motion Bt, as defined in [2], can be handle by an R–valued Wiener process bt, in the sense that Bt = Ibt ; i.e. it is actually the indicator function of a Wiener process.

Formulae connecting the multiple Stratonovich integrals with single Ogawa and Stratonovich integrals are derived. Multiple Riemann-Stieltjes integrals with respect to certain smooth approximations of the Wiener process are considered and it is shown that these integrals converge to multiple Stratonovich integrals as the approximation converges to the Wiener process.

Neural networks are applicable in identification systems from input-output data. In this report, we analyze theHammerstein-Wiener models and identify them. TheHammerstein-Wiener systems are the simplest type of block orientednonlinear systems where the linear dynamic block issandwiched in between two static nonlinear blocks, whichappear in many engineering applications; the aim of nonlinearsyst...

Econometricians are liable to regard discrete-time autoregressive moving-average (ARMA) models as approximations to continuous-time stochastic differential equations. (For a recent exposition of this point of view, see Sims 2010.) In common with other statisticians, they tend to assume that the differential equations are powered by the increments of a Wiener process. A Wiener process is formed ...

We consider a time varying wireless fading channel, equalized by an LMS linear equalizer in decision directed mode (DD-LMS-LE). We study how well this equalizer tracks the optimal Wiener equalizer. Initially we study a fixed channel. For a fixed channel, we obtain the existence of DD attractors near the Wiener filter at high SNRs using an ODE (Ordinary Differential Equation) approximating the D...

An α-Wiener bridge is a one-parameter generalization of the usual Wiener bridge, where the parameter α > 0 represents a mean reversion force to zero. We generalize the notion of α-Wiener bridges to continuous functions α : [0, T ) → R. We show that if the limit limt↑T α(t) exists and is positive, then a general α-Wiener bridge is in fact a bridge in the sense that it converges to 0 at time T wi...

In this paper we prove that the centered three-dimensional Wiener sausage can be strongly approximated by a one-dimensional Brownian motion running at a suitable time clock. The strong approximation gives all possible laws of iterated logarithm as well as the convergence in law in terms of process for the normalized Wiener sausage. The proof relies on Le Gall [10]’s fine L-norm estimates betwee...

The nonrelativistic standard model for a continuous, one-parameter diffusion process in position space is the Wiener process. As is well known, the Gaussian transition probability density function (PDF) of this process is in conflict with special relativity, as it permits particles to propagate faster than the speed of light. A frequently considered alternative is provided by the telegraph equa...

The detection of continuous gravitational-wave signals requires to account for the motion of the detector with respect to the solar system barycenter in the data analysis. In order to search efficiently for such signals by means of the fast Fourier transform the data needs to be transformed from the topocentric time to the barycentric time by means of resampling. The resampled data form a non-s...