The failure rate in reliability: Approximations and bounds.
The failure rate in reliability. Numerical treatment.
The first exit of almost strongly recurrent semi-Markov processes
Let , 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 [; j ∈ J] be the stationary p.d. of the embedded Markov chain. In terms of the averaged...
The scaling limits of a heavy tailed Markov renewal process
In this paper we consider heavy tailed Markov renewal processes and we prove that, suitably renormalised, they converge in law towards the -stable regenerative set. We then apply these results to the strip wetting model which is a random walk constrained above a wall and rewarded or penalized when it hits the strip where is a given positive number. The convergence result that we establish allows to characterize the scaling limit of this process at criticality.
The superposition of two independent Markov renewal processes
Théorie du renouvellement pour des chaînes semi-markoviennes transientes
Topics in Markov Additive Processes.
Two parallel finite queues with simultaneous services and Markovian arrivals.