Sentence examples for maximal inequality of from inspiring English sources

Then we conclude applying the sharp maximal inequality of Theorem 12 that in fact allows to estimate, in an integral way, oscillations of the gradient.

Assume that the Rosenthal type maximal inequality of (Y_{nj}=Y_{j}I{vert Y_{j}vert leq f(n)}) holds true for (r=2).

Assume that the Rosenthal type maximal inequality of (Y_{xj}=-xI{Y_{j}<-x}+Y_{j}I{vert Y_{j}vert leq x}+xI{Y_{j}>x}) holds for the above r and all (x> 0).

(3.6) If ({X_{i}, ige 1}) is a sequence of NA random variables, then from the maximal inequality of NA random variables (see [8, Theorem 2]), the condition (3.5) can be weakened by (3.6).

Assume that the Rosenthal type maximal inequality of (Y_{xj}=-xI{Y_{j}<-x}+Y_{j}I{vert Y_{j}vert leq x}+xI{Y_{j}>x}) holds for any (qgeq2) and (x> 0).

If ({X_{i}, ige 1}) is a sequence of NA random variables satisfying the assumptions of Theorem 2.2, then from the maximal inequality of NA random variables (see [8, Theorem 2]), the condition (2.4) can be weakened by (2.1).

One is the maximal inequality for pth power of the norm of stochastic convolution integrals.

Brzezniak et al. [7] have derived a maximal inequality for pth power of the norm of stochastic convolutions driven by Poisson random measures.

For a sequence of dependent square integrable random variables and a sequence of positive numbers, we establish a maximal inequality for weighted sums of dependent random variables.

We also establish a Hájek-Rényi-type maximal inequality for multidimensional arrays of random elements and some maximal moment inequalities for arrays of dependent random elements.

Theorem 2.1 provides a Hájek-Rényi-type maximal inequality for multidimensional arrays of random elements.