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The method of stochastic exponentials for large deviations

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  • Puhalskii, A.

Abstract

We present a method for proving the large-deviation principle for processes with paths in the Skorohod space which is analogous to the method of stochastic exponentials in weak convergence. It is applied to derive new results on large deviations for semimartingales as well as for processes with independent increments.

Suggested Citation

  • Puhalskii, A., 1994. "The method of stochastic exponentials for large deviations," Stochastic Processes and their Applications, Elsevier, vol. 54(1), pages 45-70, November.
    • Handle: RePEc:eee:spapps:v:54:y:1994:i:1:p:45-70
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    Cited by:

    1. Xue, Xiaofeng & Zhao, Linjie, 2024. "Moderate deviations for the current and tagged particle in symmetric simple exclusion processes," Stochastic Processes and their Applications, Elsevier, vol. 167(C).
    2. Klebaner, F. C. & Liptser, R., 1999. "Moderate deviations for randomly perturbed dynamical systems," Stochastic Processes and their Applications, Elsevier, vol. 80(2), pages 157-176, April.
    3. Xue, Xiaofeng, 2021. "Moderate deviations of density-dependent Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 140(C), pages 49-80.
    4. Chen, Lei & Gao, Fuqing, 2013. "Moderate deviation principle for Brownian motions on the unit sphere in Rd," Statistics & Probability Letters, Elsevier, vol. 83(11), pages 2486-2491.
    5. Anatolii A. Puhalskii & Alexander A. Vladimirov, 2007. "A Large Deviation Principle for Join the Shortest Queue," Mathematics of Operations Research, INFORMS, vol. 32(3), pages 700-710, August.
    6. Dembo, Amir & Zajic, Tim, 1995. "Large deviations: From empirical mean and measure to partial sums process," Stochastic Processes and their Applications, Elsevier, vol. 57(2), pages 191-224, June.
    7. Salim Bouzebda & Yousri Slaoui, 2023. "Nonparametric Recursive Estimation for Multivariate Derivative Functions by Stochastic Approximation Method," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 658-690, February.
    8. Franziska Kühn & René L. Schilling, 2016. "Moderate Deviations and Strassen’s Law for Additive Processes," Journal of Theoretical Probability, Springer, vol. 29(2), pages 632-652, June.
    9. Bouzebda, Salim & Slaoui, Yousri, 2019. "Large and moderate deviation principles for recursive kernel estimators of a regression function for spatial data defined by stochastic approximation method," Statistics & Probability Letters, Elsevier, vol. 151(C), pages 17-28.

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