A conditioned local limit theorem for non-negative random matrices

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 $[b,b+\ell ]\subset {\mathbb{R}}^{\ast +}$ at time $n$.

References in corpus (2)

• Invariance principles for random walks conditioned to stay positive
• On the rate of convergence in the weak invariance principle for dependent random variables with applications to Markov chains

Cited by in corpus (1)

• The survival probability of a weakly subcritical multitype branching process in iid random environment