arXiv subjects

Jianzhang Mei

Publications and source records attributed to Jianzhang Mei.

2 recordsLinked to original sources

arXiv2025

Convergence to Stable Laws and a Local Limit Theorem for Products of Positive Random Matrices

We consider the products $G_n = A_n \cdots A_1$ of independent and identical distributed nonnegative $d \times d$ matrices $(A_i)_{i \geq 1}$. For any starting point $x \in \mathbb{R}_+^d$ with unit norm, we establish the convergence to a stable law for the norm cocycle $\log | G_nx |$, jointly with its direction $G_n \cdot x = G_n x / | G_n x |$. We also prove a local limit theorem for the couple $ (\log |G_nx|, G_n \cdot x)$, and find the exact rate of its convergence.

math.PR↗

arXiv2024

Support, absolute continuity and harmonic moments of fixed points of the multivariate smoothing transform

Consider the multivariate smoothing transform fixed-point equation: $η=$ law of $ \sum_{i=1}^N A_i Z_i$, where $N \geq 0$ is a random integer, $(A_i)_{i \geq 1}$ are $d \times d$ random nonnegative matrices, $(Z_i)_{i \geq 1}$ is a sequence of $\mathbb{R}_+^d$-valued random variables independent of $(N, A_1, A_2, \cdots)$, and all $Z_i$ have the same law $η$. For each fixed point $η$, under suitable conditions, we describe its support, establish its absolute continuity, and prove the existence of its harmonic moments.

math.PR↗