Rare-event analysis of modulated Ornstein-Uhlenbeck processes

Abstract : This paper studies Ornstein-Uhlenbeck (OU) processes in a random environment. The OU model has found widespread use in networking, as a Gaussian approximation of the user-level dynamics that allows explicit analysis; adding modulation to it allows incorporating phenomena in which the users' activity level is affected by exogenous factors. The focus lies on rare-event analysis: under a specific scaling of the parameters involved , we establish the large deviations asymptotics of the probability that the process reaches an extreme value. The decay rate of this probability is generally only implicitly available (as the solution to a variational problem), but specializing to the case of Markov modulation we succeed in devising efficient numerical procedures.
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H M Jansen, M Mandjes, Koen de Turck, Sabine Wittevrongel. Rare-event analysis of modulated Ornstein-Uhlenbeck processes. Performance Evaluation, Elsevier, 2017, 112, pp.1 - 14. ⟨10.1016/j.peva.2017.02.002⟩. ⟨hal-01580377⟩

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