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Large deviations for high minima of Gaussian processes with nonnegatively correlated increments

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  • Selk, Zachary

Abstract

In this article we prove large deviations principles for high minima of Gaussian processes with nonnegatively correlated increments on arbitrary intervals. Furthermore, we prove large deviations principles for the increments of such processes on intervals [a,b] where b−a is either less than the increment or twice the increment, assuming stationarity of the increments. As a chief example, we consider fractional Brownian motion and fractional Gaussian noise for H≥1/2.

Suggested Citation

  • Selk, Zachary, 2024. "Large deviations for high minima of Gaussian processes with nonnegatively correlated increments," Statistics & Probability Letters, Elsevier, vol. 206(C).
    • Handle: RePEc:eee:stapro:v:206:y:2024:i:c:s0167715223002250
    DOI: 10.1016/j.spl.2023.110001
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    References listed on IDEAS

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    1. Jim Gatheral & Thibault Jaisson & Mathieu Rosenbaum, 2018. "Volatility is rough," Quantitative Finance, Taylor & Francis Journals, vol. 18(6), pages 933-949, June.
    2. Chakrabarty, Arijit & Samorodnitsky, Gennady, 2018. "Asymptotic behaviour of high Gaussian minima," Stochastic Processes and their Applications, Elsevier, vol. 128(7), pages 2297-2324.
    3. Christian Bayer & Peter Friz & Jim Gatheral, 2016. "Pricing under rough volatility," Quantitative Finance, Taylor & Francis Journals, vol. 16(6), pages 887-904, June.
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    Keywords

    Large deviations; Gaussian processes;

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