Summability of Double Independent Random Variables

Tauberian Theorems for Summability Transforms

we then write sn → s(A), where A is the A method of summability. Appropriate choices of A= [an,k] for n,k ≥ 0 give the classical methods [2]. In this paper, we present various summability analogs of the strong law of large numbers (SLLN) and their rates of convergence in an unified setting, beyond the class of random-walk methods. A convolution summability method introduced in the next section ...

On absolute generalized Norlund summability of double orthogonal series

In the paper [Y. Okuyama, {it On the absolute generalized N"{o}rlund summability of orthogonal series},Tamkang J. Math. Vol. 33, No. 2, (2002), 161-165] the author has found some sufficient conditions under which an orthogonal seriesis summable $|N,p,q|$ almost everywhere. These conditions are expressed in terms of coefficients of the series. It is the purpose ofthis paper to extend this result...

Electronic Communications in Probability Strong Laws and Summability for Sequences of '-mixing Random Variables in Banach Spaces

In this note the almost sure convergence of stationary, '-mixing sequences of random variables with values in real, separable Banach spaces according to summability methods is linked to the fullllment of a certain integrability condition generalizing and extending the results for i.i.d. sequences. Furthermore we give via Baum-Katz type results an estimate for the rate of convergence in these laws.

Strong Laws and Summability for Sequences of Φ-mixing Random Variables in Banach Spaces

In this note the almost sure convergence of stationary, φ-mixing sequences of random variables with values in real, separable Banach spaces according to summability methods is linked to the fulfillment of a certain integrability condition generalizing and extending the results for i.i.d. sequences. Furthermore we give via Baum-Katz type results an estimate for the rate of convergence in these l...

On Nörlünd Summability of Random Variables to Zero