Results 11  20
of
5,987
A remark on divisor weighted sums
"... Let {an} be a sequence of nonnegative real numbers. Under very mild hypotheses, we obtain upper bounds of the expected order of magnitude for sums of the form n≤x anτr(n), where τr(n) is the rfold divisor function. This sharpens previous estimates of Friedlander and Iwaniec. The proof uses combinat ..."
Abstract
 Add to MetaCart
Let {an} be a sequence of nonnegative real numbers. Under very mild hypotheses, we obtain upper bounds of the expected order of magnitude for sums of the form n≤x anτr(n), where τr(n) is the rfold divisor function. This sharpens previous estimates of Friedlander and Iwaniec. The proof uses
STRONG APPROXIMATIONS OF WEIGHTED SUMS OF RANDOM VARIABLES
"... We develop strong approximations of weighted sums of random variables. The consequences of these approximations are an estimation of the ProhorovLevy distance between weighted partial sums and their limit processes and the functional law of the iterated logarithm. We obtain a generalization of Gapo ..."
Abstract
 Add to MetaCart
We develop strong approximations of weighted sums of random variables. The consequences of these approximations are an estimation of the ProhorovLevy distance between weighted partial sums and their limit processes and the functional law of the iterated logarithm. We obtain a generalization
A NOTE ON CONVERGENCE OF WEIGHTED SUMS OF RANDOM VARIABLES
, 1984
"... ABSTRACT. Under uniform integrability condition, some Weak Laws of large numbers are established for weighted sums of random variables generalizing results of Rohatgi, Pruitt and Khintchine. Some Strong Laws of Large Numbers are proved for weighted sums of pairwise independent random variables gener ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
ABSTRACT. Under uniform integrability condition, some Weak Laws of large numbers are established for weighted sums of random variables generalizing results of Rohatgi, Pruitt and Khintchine. Some Strong Laws of Large Numbers are proved for weighted sums of pairwise independent random variables
Weighted sum formula for multiple zeta values
"... Abstract. The sum formula is a basic identity of multiple zeta values that expresses a Riemann zeta value as a homogeneous sum of multiple zeta values of a given dimension. This formula was already known to Euler in the dimension two case, conjectured in the early 1990s for higher dimensions and the ..."
Abstract

Cited by 9 (3 self)
 Add to MetaCart
and then proved by Granville and Zagier independently. Recently a weighted form of Euler’s formula was obtained by Ohno and Zudilin. We generalize it to a weighted sum formula for multiple zeta values of all dimensions. 1.
Weighted sums of subexponential random variables and their maxima
 Adv. in Appl. Probab
"... Let {Xk, k = 1, 2,...} be a sequence of independent random variables with common subexponential distribution F, and let {wk, k = 1, 2,...} be a sequence of positive numbers. Under some mild summability conditions, we establish simple asymptotic estimates for the extreme tail probabilities of the wei ..."
Abstract

Cited by 6 (2 self)
 Add to MetaCart
of the weighted sum ∑n k=1 wkXk and m of the maxima of weighted sums max1≤m≤n k=1 wkXk, subject to the requirement that they should hold uniformly for n = 1, 2,.... A direct application of the result is to risk analysis, where the ruin probability is to be evaluated for a company having the gross loss Xk during
Efficiently approximating weighted sums with exponentially many terms
 In Proceedings of the Fourteenth Annual Conference on Computational Learning Theory
, 2001
"... Multiplicative weightupdate algorithms such as Winnow and Weighted Majority have been studied extensively due to their online mistake bounds ’ logarithmic dependence on N, the total number of inputs, which allows them to be applied to problems where N is exponential. However, a large N requires te ..."
Abstract

Cited by 10 (4 self)
 Add to MetaCart
techniques to efficiently compute the weighted sums of inputs to these algorithms. In special cases, the weighted sum can be exactly computed efficiently, but for numerous problems such an approach seems infeasible. Thus we explore applications of Markov chain Monte Carlo (MCMC) methods to estimate the total
Abstract Analysis and Synthesis of WeightedSum Functions
"... A weightedsum (WS) function computes the sum of selected integers. This paper considers a design method for WS functions by LUT cascades. In particular, it derives upper bounds on the column multiplicities of decomposition charts for WS functions. From these, we can estimate the size of LUT cascade ..."
Abstract
 Add to MetaCart
A weightedsum (WS) function computes the sum of selected integers. This paper considers a design method for WS functions by LUT cascades. In particular, it derives upper bounds on the column multiplicities of decomposition charts for WS functions. From these, we can estimate the size of LUT
Results 11  20
of
5,987