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Large deviations for Markov-modulated diffusion processes with rapid switching

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  • Huang, Gang
  • Mandjes, Michel
  • Spreij, Peter

Abstract

In this paper, we study small noise asymptotics of Markov-modulated diffusion processes in the regime that the modulating Markov chain is rapidly switching. We prove the joint sample-path large deviations principle for the Markov-modulated diffusion process and the occupation measure of the Markov chain (which evidently also yields the large deviations principle for each of them separately by applying the contraction principle). The structure of the proof is such that we first prove exponential tightness, and then establish a local large deviations principle (where the latter part is split into proving the corresponding upper bound and lower bound).

Suggested Citation

  • Huang, Gang & Mandjes, Michel & Spreij, Peter, 2016. "Large deviations for Markov-modulated diffusion processes with rapid switching," Stochastic Processes and their Applications, Elsevier, vol. 126(6), pages 1785-1818.
    • Handle: RePEc:eee:spapps:v:126:y:2016:i:6:p:1785-1818
    DOI: 10.1016/j.spa.2015.12.005
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    References listed on IDEAS

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    1. Huang, Gang & Mandjes, Michel & Spreij, Peter, 2014. "Weak convergence of Markov-modulated diffusion processes with rapid switching," Statistics & Probability Letters, Elsevier, vol. 86(C), pages 74-79.
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    Cited by:

    1. O. J. Boxma & E. J. Cahen & D. Koops & M. Mandjes, 2019. "Linear Stochastic Fluid Networks: Rare-Event Simulation and Markov Modulation," Methodology and Computing in Applied Probability, Springer, vol. 21(1), pages 125-153, March.
    2. Florian Simatos & Alain Simonian, 2020. "Mobility can drastically improve the heavy traffic performance from $$\frac{1}{1-\varrho }$$11-ϱ to $$\log (1/(1-\varrho ))$$log(1/(1-ϱ))," Queueing Systems: Theory and Applications, Springer, vol. 95(1), pages 1-28, June.
    3. Nguyen, Dang Hai & Yin, George & Zhu, Chao, 2017. "Certain properties related to well posedness of switching diffusions," Stochastic Processes and their Applications, Elsevier, vol. 127(10), pages 3135-3158.
    4. Braunsteins, Peter & Mandjes, Michel, 2023. "The Cramér-Lundberg model with a fluctuating number of clients," Insurance: Mathematics and Economics, Elsevier, vol. 112(C), pages 1-22.
    5. Blom, Joke & De Turck, Koen & Mandjes, Michel, 2017. "Refined large deviations asymptotics for Markov-modulated infinite-server systems," European Journal of Operational Research, Elsevier, vol. 259(3), pages 1036-1044.

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