Rare-event analysis of modulated Ornstein–Uhlenbeck processes
- Author
- Hermanus Marinus Jansen (UGent) , Michel Mandjes, Koen De Turck (UGent) and Sabine Wittevrongel (UGent)
- Organization
- 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.
- Keywords
- large deviations asymptotics, random environment, Markov modulation, Ornstein-Uhlenbeck process, Hamilton-Jacobi-Bellman equations
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-8524250
- MLA
- Jansen, Hermanus Marinus, et al. “Rare-Event Analysis of Modulated Ornstein–Uhlenbeck Processes.” PERFORMANCE EVALUATION, vol. 112, Elsevier BV, 2017, pp. 1–14, doi:10.1016/j.peva.2017.02.002.
- APA
- Jansen, H. M., Mandjes, M., De Turck, K., & Wittevrongel, S. (2017). Rare-event analysis of modulated Ornstein–Uhlenbeck processes. PERFORMANCE EVALUATION, 112, 1–14. https://doi.org/10.1016/j.peva.2017.02.002
- Chicago author-date
- Jansen, Hermanus Marinus, Michel Mandjes, Koen De Turck, and Sabine Wittevrongel. 2017. “Rare-Event Analysis of Modulated Ornstein–Uhlenbeck Processes.” PERFORMANCE EVALUATION 112: 1–14. https://doi.org/10.1016/j.peva.2017.02.002.
- Chicago author-date (all authors)
- Jansen, Hermanus Marinus, Michel Mandjes, Koen De Turck, and Sabine Wittevrongel. 2017. “Rare-Event Analysis of Modulated Ornstein–Uhlenbeck Processes.” PERFORMANCE EVALUATION 112: 1–14. doi:10.1016/j.peva.2017.02.002.
- Vancouver
- 1.Jansen HM, Mandjes M, De Turck K, Wittevrongel S. Rare-event analysis of modulated Ornstein–Uhlenbeck processes. PERFORMANCE EVALUATION. 2017;112:1–14.
- IEEE
- [1]H. M. Jansen, M. Mandjes, K. De Turck, and S. Wittevrongel, “Rare-event analysis of modulated Ornstein–Uhlenbeck processes,” PERFORMANCE EVALUATION, vol. 112, pp. 1–14, 2017.
@article{8524250,
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.}},
author = {{Jansen, Hermanus Marinus and Mandjes, Michel and De Turck, Koen and Wittevrongel, Sabine}},
issn = {{0166-5316}},
journal = {{PERFORMANCE EVALUATION}},
keywords = {{large deviations asymptotics,random environment,Markov modulation,Ornstein-Uhlenbeck process,Hamilton-Jacobi-Bellman equations}},
language = {{eng}},
pages = {{1--14}},
publisher = {{Elsevier BV}},
title = {{Rare-event analysis of modulated Ornstein–Uhlenbeck processes}},
url = {{http://dx.doi.org/10.1016/j.peva.2017.02.002}},
volume = {{112}},
year = {{2017}},
}
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