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Comparison theorems for small deviations of weighted series

Rozovsky L. V.

Probability and Mathematical Statistics

2012

Vol. 32, Fasc. 1

117--130

We study comparison theorems for small deviation probabilities of weighted series and obtain more refined versions of the known comparison results. In particular, the following consequence is obtained immediately from Theorem 2.1 of the paper. Let a positive random variable X belong to the domain of attraction of a stable law with an index greater than one and let its distribution function be regularly varying at zero with an exponent β > 0. If {Xn}n1 are independent copies of X, and {an} and {bn} are positive summable sequences such that..[formula].

Comparison theorems for the oscillation of higher order neutral delay diference equations

Zhou Y., Zhang B. G.

Demonstratio Mathematica

2002

Vol. 35, nr 3

545-555

We obtain a necessary and sufficient condition for the oscillation of the higher order neutral delay difference equation m(Xn -pnxn-r) + f(n, xg1(n),xg2(n), ...,xg1(n))=0 where m > 1 is an odd integer. As some application of this result, we estabilish three comparison theorems for the oscillation of the above equation.

Comparison theorems for n-th order nonlinear differential inequalities with deviating argument

Seman J.

Fasciculi Mathematici

1999

Nr 29

113-124

This paper deals with comparison theorems for oscillatorineess all solutions of the n-th order nonlinear differential inequalities with quasiderivativer and deviatimg argument of a form [formula]