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Preprints, Working Papers, ... Year : 2023

A conditioned local limit theorem for non-negative random matrices

(1) ,
1
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 $n$.
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Dates and versions

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

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