A conditioned local limit theorem for non-negative random matrices - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year : 2023

## A conditioned local limit theorem for non-negative random matrices

M. Peigné
Thi da Cam Pham

#### Abstract

Let $(S_n)_n$ be the random process on $\mathbb R$ driven by the product of i.i.d. non-negative random matrices and $\tau$ 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 $n$.

#### Domains

Mathematics [math] Probability [math.PR]

### Dates and versions

hal-03939554 , version 1 (15-01-2023)

### Identifiers

• HAL Id : hal-03939554 , version 1
• ARXIV :

### Cite

M. Peigné, Thi da Cam Pham. A conditioned local limit theorem for non-negative random matrices. 2023. ⟨hal-03939554⟩

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