### The first exit of almost strongly recurrent semi-Markov processes

Let $\left(\xb7\right)$, n ∈ N, be a sequence of homogeneous semi-Markov processes (HSMP) on a countable set K, all with the same initial p.d. concentrated on a non-empty proper subset J. The subrenewal kernels which are restrictions of the corresponding renewal kernels $$ on K×K to J×J are assumed to be suitably convergent to a renewal kernel P (on J×J). The HSMP on J corresponding to P is assumed to be strongly recurrent. Let [${\pi}_{j}$; j ∈ J] be the stationary p.d. of the embedded Markov chain. In terms of the averaged...