We establish some conditions for stochastic equality of two nonnegative random variables which are ordered with respect to variability ordering or with respect to mean residual life ordering or with respect to second order stochastic ordering.

We obtain a new generalization of Chebyshev's inequality for random elements taking values in a separable Hilbert space.

Maximal inequalities have been derived earlier using the upcrossing inequalities for demimartingales and the down-crossing inequalities for N-demimartingales. We give an alternate approach for deriving maximal inequalities for non-negative demisubmartingales using elementary inequalities for...

In this paper, we establish some maximal inequalities for N-demimartingale. The maximal inequality for N-demimartingale is used as a key inequality to establish other results including the strong law of large numbers, strong growth rate and the integrability of supremum for N-demimartingale.

We obtain two characterizations of the Gaussian distribution on a Hilbert space from samples of random size.