arXiv subjects

Thi da Cam Pham

Publications and source records attributed to Thi da Cam Pham.

2 recordsLinked to original sources

arXiv2026

A local limit theorem for nonlattice multidimensional random walks in cones

We study the asymptotic behavior of a nonlattice random walk in a general cone of $R^d$ . Following the approach initiated by D. Denisov and V. Wachtel in [8], we use a strong approximation of random walks by the Brownian motion and prove local limit theorems, combining integral theorems for random walks in cones with classical theorems for unrestricted random walks.

math.PR↗

arXiv2023

A conditioned local limit theorem for non-negative random matrices

Let $(S_n)_n$ be the random process on $\mathbb R$ driven by the product of i.i.d. non-negative random matrices and $τ$ its exit time from $]0, +\infty[$. By using the adapted strategy initiated by D. Denisov and V. Wachtel, we obtain an asymptotic estimate and bounds of the probability that the process $(S_k)_k$ remains non negative up to time $n$ and simultaneously belongs to some compact set $[b, b+\ell ]\subset \mathbb R^{*+}$ at time $n$.

math.PR↗