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On the upper bound in Varadhan’s Lemma

Author

Listed:
  • Jansen, H.M.
  • Mandjes, M.R.H.
  • De Turck, K.
  • Wittevrongel, S.

Abstract

In this paper, we generalize the upper bound in Varadhan’s Lemma. The standard formulation of Varadhan’s Lemma contains two important elements, namely an upper semicontinuous integrand and a rate function with compact sublevel sets. However, motivated by results from queueing theory, in this paper we do not assume that rate functions have compact sublevel sets. Moreover, we drop the assumption that the integrand is upper semicontinuous and replace it by a weaker condition. We prove that the upper bound in Varadhan’s Lemma still holds under these weaker conditions. Additionally, we show that only measurability of the integrand is required when the rate function is continuous.

Suggested Citation

  • Jansen, H.M. & Mandjes, M.R.H. & De Turck, K. & Wittevrongel, S., 2015. "On the upper bound in Varadhan’s Lemma," Statistics & Probability Letters, Elsevier, vol. 103(C), pages 24-29.
    • Handle: RePEc:eee:stapro:v:103:y:2015:i:c:p:24-29
    DOI: 10.1016/j.spl.2015.04.005
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    Cited by:

    1. H. M. Jansen & M. R. H. Mandjes & K. De Turck & S. Wittevrongel, 2016. "A large deviations principle for infinite-server queues in a random environment," Queueing Systems: Theory and Applications, Springer, vol. 82(1), pages 199-235, February.

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