Abstract
In this paper, we first prove Schilder’s theorem in Hölder norm (0 ≤ α < 1) with respect to C r,p -capacity. Then, based on this result, we further prove a sharpening of large deviation principle for increments of fractional Brownian motion for C r,p -capacity in the stronger topology.
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Supported by NSFC (Grant Nos. 11271013, 61273074, 61201065, 61203219, 11471104) and the Fundamental Research Funds for the Central Universities, HUST (Grant Nos. 2012QN028 and 2014TS066), IRTSTHN (Grant No. 14IRSTHN023), PhD research startup foundation of He’nan Normal University (Grant No. 5101019170120), Youth Science Foundation of He’nan Normal University (Grant No. 5101019279032)
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Xu, J., Zhu, Y.M. & Liu, J.C. Quasi sure large deviation for increments of fractional Brownian motion in Hölder norm. Acta. Math. Sin.-English Ser. 31, 913–920 (2015). https://doi.org/10.1007/s10114-015-3560-x
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DOI: https://doi.org/10.1007/s10114-015-3560-x