A real square matrix satisfies the weak Hawkins-Simon condition if its leading principal minors are positive (the condition was first studied by the French mathematician Maurice Potron). Three characterizations are given. Simple sufficient conditions ensure that the condition holds after a suitable reordering of columns. A full characterization of this set of matrices should take into account t...

We introduce a new class of Backward Stochastic Differential Equations in which the T -terminal value YT of the solution (Y, Z) is not fixed as a random variable, but only satisfies a weak constraint of the form E[Ψ(YT )] ≥ m, for some (possibly random) non-decreasing map Ψ and some threshold m. We name them BSDEs with weak terminal condition and obtain a representation of the minimal time t-va...

In this paper, we derive a necessary and sufficient condition on the parameters of the Hypergeomet-ric distribution for weak convergence to a Normal limit. We establish a Berry-Esseen theorem for the Hypergeometric distribution solely under this necessary and sufficient condition. We further derive a nonuniform Berry-Esseen bound where the tails of the difference between the Hypergeo-metric and...

In this paper, we introduce and study a new iterative scheme toapproximate a common xed point for a nite family of generalized asymptoticallyquasi-nonexpansive nonself-mappings in Banach spaces. Several strong and weakconvergence theorems of the proposed iteration are established. The main resultsobtained in this paper generalize and rene some known results in the currentliterature.

This paper concerns the macroscopic behavior of solutions to parabolic equations with large, highly oscillatory, random potential. When the correlation function of the random potential satisfies a specific integrability condition, we show that the random solution converges, as the correlation length of the medium tends to zero, to the deterministic solution of a homogenized equation in dimensio...

This paper investigates weak convergence of U -statistics via approximation in probability. The classical condition that the second moment of the kernel of the underlying U -statistic exists is relaxed to having 43 moments only (modulo a logarithmic term). Furthermore, the conditional expectation of the kernel is only assumed to be in the domain of attraction of the normal law (instead of the c...