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Large deviations and the Strassen theorem in Hölder norm

Author

Listed:
  • Baldi, P.
  • Ben Arous, G.
  • Kerkyacharian, G.

Abstract

We prove that Schilder's theorem, giving large deviations estimates for the Brownian motion multiplied by a small parameter, still holds with the sup-norm replaced by any Hölder norm with exponent. We produce examples which show that this is effectively a stronger result and, as an application, we prove Strassen's Iterated Logarithm Law in these stronger topologies.

Suggested Citation

  • Baldi, P. & Ben Arous, G. & Kerkyacharian, G., 1992. "Large deviations and the Strassen theorem in Hölder norm," Stochastic Processes and their Applications, Elsevier, vol. 42(1), pages 171-180, August.
    • Handle: RePEc:eee:spapps:v:42:y:1992:i:1:p:171-180
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    Cited by:

    1. Archil Gulisashvili, 2017. "Large deviation principle for Volterra type fractional stochastic volatility models," Papers 1710.10711, arXiv.org, revised Aug 2018.
    2. Liu, Yonghong & Li, Luoqing & Wan, Chenggao, 2009. "The rate of convergence for increments of a Brownian motion in Hölder norm," Statistics & Probability Letters, Elsevier, vol. 79(12), pages 1463-1472, June.
    3. Gao, Fuqing & Jiang, Hui, 2010. "Large deviations for stochastic differential equations driven by G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 120(11), pages 2212-2240, November.
    4. Aleksandar Arandjelovi'c & Thorsten Rheinlander & Pavel V. Shevchenko, 2021. "Importance sampling for option pricing with feedforward neural networks," Papers 2112.14247, arXiv.org, revised Jun 2023.
    5. Hu, Yi-Jun, 1997. "A large deviation principle for small perturbations of random evolution equations in Hölder norm," Stochastic Processes and their Applications, Elsevier, vol. 68(1), pages 83-99, May.
    6. Gulisashvili, Archil, 2021. "Time-inhomogeneous Gaussian stochastic volatility models: Large deviations and super roughness," Stochastic Processes and their Applications, Elsevier, vol. 139(C), pages 37-79.
    7. Norvaisa, R., 1995. "The Strassen law of the iterated logarithm in Banach function spaces," Statistics & Probability Letters, Elsevier, vol. 25(1), pages 1-8, October.

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