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J. Lenzi

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Preprint Aug 2026

Breiman's conjecture and normalized jumps of subordinators

We prove Breiman's conjecture under the first-moment assumption. Let $Y_1,Y_2,\ldots$ be iid nonnegative random variables with $\mathbb P\{Y_1>0\}>0$, normalized by their sum. If the resulting randomly weighted sum converges to a nondegenerate law for one fixed integrable, nonconstant mark distribution, then the tail o...

J. Lenzi · 1 citation · ⚡1

Preprint Aug 2026

Power-sum convergence for randomly weighted means and Breiman's conjecture

We establish a power-sum convergence principle for randomly weighted means. Let $P(t)=(P_j(t))$ be random finitely supported subprobability weight sequences, independent of iid centered integrable marks. If the expected total mass converges and the expected power sum of some order $r\in(0,1)$ is uniformly bounded, then...

J. Lenzi · 0 citations