We prove that partial sums of linear multiparameter stochastic processes can be represented as partial sums of independent innovations plus components that are uniformly of smaller order. This representation is exploited to establish functional central limit theorems and strong approximations for random fields.

An explicit upper bound on the tail probabilities for the normalized Rademacher sums is given. This bound, which is best possible in a certain sense, is asymptotically equivalent to the corresponding tail probability of the standard normal distribution, thus affirming a longstanding conjecture by Efron. Applications to sums of general centered uniformly bounded independent random variables and ...

For arrays of independent Pareto random variables, this paper establishes complete convergence for weighted partial sums for the smaller order statistics within each row. This result improves on past strong laws. Moreover, it shows that we can obtain a finite nonzero limit for our normalized partial sums under complete convergence even though the first moment of our order statistics is infinite.

The asymptotic density of random permutations with given properties of the kth shortest cycle length is examined. The approach is based upon the saddle point method applied for appropriate sums of independent random variables.

Introduction: The present study aimed to find an appropriate method toinform senior high school students to correctly select their academic field ofstudy and their intentions.Methods: This is a descriptive-analytic and cross-sectional study. A verifiedquestionnaire was given to a total of 2600 students selected by stratified random sampling method (ten different colleges and entrance year from ...

We find the extremal configuration for the p-moment of sums of independent positive random variables while constraining the sum of the expectations of the random variables and the sum of their p-moments.

Many fundamental questions in additive number theory (such as Goldbach’s conjecture, Fermat’s last theorem, and the Twin Primes conjecture) can be expressed in the language of sum and difference sets. As a typical pair of elements contributes one sum and two differences, we expect that |A−A| > |A+A| for a finite set A. However, in 2006 Martin and O’Bryant showed that a positive proportion of su...

The paper deals with a problem proposed by Uriel Feige in 2005: if X1, . . . , Xn is a set of independent nonnegative random variables with expectations equal to 1, is it true that P ( ∑n i=1 Xi < n + 1) > 1 e ? He proved that P ( ∑n i=1Xi < n + 1) > 1 13 . In this paper we prove that infimum of the P ( ∑n i=1Xi < n + 1) can be achieved when all random variables have only two possible values, a...

Stretched exponential probability density functions (pdf), having the form of the exponential of minus a fractional power of the argument, are commonly found in turbulence and other areas. They can arise because of an underlying random multiplicative process. For this, a theory of extreme deviations is developed, devoted to the far tail of the pdf of the sum X of a finite number n of independen...

We study asymptotic behavior of the sums ZN,m(β) determined by the formula ZN,m(β) = N