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We obtain two characterizations of the Gaussian distribution on a Hilbert space from samples of random size. [ABSTRACT FROM AUTHOR]

Abstract: We prove some conditional Borel–Cantelli lemmas for sequences of random variables. As an application, a conditional version of the weighted Borel–Cantelli lemma is obtained. [Copyright &y& Elsevier]

Abstract: Agbeko (1986) proved some concave function inequalities for sub-(super-) martingales. Christofides (2003) obtained some maximal inequalities for concave Young functions for -demimartingales. In this paper, we will further extend these results to the cases of demimartingales and -demimartingales. Our results also generalize and improve partial results of Wang et al. (2010, 2011) . [Copyright &y& Elsevier]

Abstract: We obtain lower and upper bounds for the absolute values of characteristic functions of multivariate distributions F and also derive a lower bound on the norm of the zeroes of a characteristic function in terms of moments of the norm of the random vector with distribution F. Similar results are obtained for characteristic functions of probability measures on a separable Hilbert space. [Copyright &y& Elsevier]

The asymptotic properties of the least squares estimator of the cusp in some nonlinear nonregular regression models is investigated via the study of the weak convergence of the least squares process generalizing earlier results in Prakasa Rao (Statist. Probab. Lett. 3 (1985) 15). [Copyright &y& Elsevier]