Borel methods of summability and ergodic theorems
Passing from Cesàro means to Borel-type methods of summability we prove some ergodic theorem for operators (acting in a Banach space) with spectrum contained in ℂ∖(1,∞).
Passing from Cesàro means to Borel-type methods of summability we prove some ergodic theorem for operators (acting in a Banach space) with spectrum contained in ℂ∖(1,∞).
To derive a Baum-Katz type result, a Chover-type law of the iterated logarithm is established for weighted sums of negatively associated (NA) and identically distributed random variables with a distribution in the domain of a stable law in this paper.
In extremal estimation theory the estimators are local or absolute extremes of functions defined on the cartesian product of the parameter by the sample space. Assuming that these functions converge uniformly, in a convenient stochastic way, to a limit function g, set estimators for the set ∇ of absolute maxima (minima) of g are obtained under the compactness assumption that ∇ is contained in a known compact U. A strongly consistent test is presented for this assumption. Moreover, when the true...
Let , , be a double array of independent and identically distributed (i.i.d.) real random variables with , and . Consider sample covariance matrices (with/without empirical centering) and , where and with , non-random symmetric non-negative definite matrix. It is proved that central limit theorems of eigenvalue statistics of and are different as with approaching a positive constant. Moreover, it is also proved that such a different behavior is not observed in the average behavior...
In the present paper, we have established the complete convergence for weighted sums of pairwise independent random variables, from which the rate of convergence of moving average processes is deduced.