Jacopo Lenzi

Breiman's conjecture and normalized jumps of subordinators

We prove Breiman's conjecture under the first-moment assumption. Let Y₁, Y₂, … be iid nonnegative random variables with ℙ{Y₁ > 0} > 0, normalized by their sum. If the resulting randomly weighted sum converges to a nondegenerate law for one fixed integrable, nonconstant mark distr...

Breiman's conjecture and normalized jumps of subordinators

We prove Breiman's conjecture under the first-moment assumption. Let Y₁, Y₂, … be iid nonnegative random variables with ℙ{Y₁ > 0} > 0, normalized by their sum. If the resulting randomly weighted sum converges to a nondegenerate law for one fixed integrable, nonconstant mark distr...

Dimension comparison for Student's statistic under symmetric unimodality

Preprint. This manuscript has not undergone journal peer review.