We assume without loss of generality that E{Xn} = 0. Let rs = i£{XnXn+s}. Then r8 = / I T edF(h), where F(X) is the spectral distribution function of the process. In §3 the spectral distribution function of any process of the form (2.2) is shown to be absolutely continuous. Finally it is shown in §4 that under some additional assumptions on the moment structure of the process the central limit ...

We consider the problem of learning the dependence of one random variable on another, from a finite string of independently identically distributed (i.i.d.) copies of the pair. The problem is first converted to that of learning a function of the latter random variable and an independent random variable uniformly distributed on the unit interval. However, this cannot be achieved using the usual ...

In this paper, several related estimation problems are addressed from a Bayesian point of view, and optimal estimators obtained for each them when some natural loss functions considered. The considered the regression curve, conditional distribution function, density, even itself. These posed in sufficiently general framework to cover continuous discrete, univariate multivariate, parametric nonp...

In this research mass transfer coefficient under jetting regime in different directions (from dispersed to continuous and continuous to dispersed phase) has been studied using an experimental setup. n-Butanol-succinic acid-water with low interfacial tension has been selected as experimental chemical system. The effects of various parameters such as jet velocity, nozzle diameter and the heig...

We deal with a weighted biharmonic problem in the unit ball of $\mathbb{R}^{4}$. The non-linearity is assumed to have critical exponential growth view Adam's type inequalities. weight $w(x)$ logarithm and potential $V$ positive continuous function on $\overline{B}$. It proved that there nontrivial weak solution this by mountain Pass Theorem. avoid loss compactness proving concentration result s...

An adaptive on-line algorithm extending the learning of learning idea is proposed and theoretically motivated. Relying only on gradient ow information it can be applied to learning continuous functions or distributions, even when no explicit loss function is given and the Hessian is not available. Its eeciency is demonstrated for a non-stationary blind separation task of acoustic signals.

An adaptive on-line algorithm extending the learning of learning idea is proposed and theoretically motivated. Relying only on gradient flow information it can be applied to learning continuous functions or distributions, even when no explicit loss function is given and the Hessian is not available. Its efficiency is demonstrated for a non-stationary blind separation task of acoustic signals.