Necessary and Sufficient Conditions for Convergence of First-Rare-Event Times for Perturbed Semi-Markov Processes
Dmitrii Silvestrov
TL;DR
This paper establishes the exact conditions under which the distribution and process of the first rare event in perturbed semi-Markov systems converge, providing a comprehensive theoretical framework.
Contribution
It provides necessary and sufficient conditions for convergence of first-rare-event times and processes in perturbed semi-Markov processes with finite phase space.
Findings
Derived conditions for convergence in distribution
Established convergence in Skorokhod J-topology
Applicable to systems with finite phase space
Abstract
Necessary and sufficient conditions for convergence in distribution of first-rare-event times and convergence in Skorokhod J-topology of first-rare-event-time processes for perturbed semi-Markov processes with finite phase space are obtained.
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Taxonomy
TopicsProbability and Risk Models · Stochastic processes and financial applications · Advanced Queuing Theory Analysis