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Chung’s law of the iterated logarithm for subfractional Brownian motion

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Abstract

Let X H = {X H(t), t ∈ ℝ+} be a subfractional Brownian motion in ℝd. We provide a sufficient condition for a self-similar Gaussian process to be strongly locally nondeterministic and show that X H has the property of strong local nondeterminism. Applying this property and a stochastic integral representation of X H, we establish Chung’s law of the iterated logarithm for X H.

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Acknowledgements

I would like to give my sincere thanks to Professor Yimin Xiao for his encouragement and stimulating discussions.

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Authors and Affiliations

  1. School of Insurance and Economics, University of International Business and Economics, Beijing, 100029, P. R. China

    Na Na Luan

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  1. Na Na Luan
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Correspondence to Na Na Luan.

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Supported by NSFC (Grant Nos. 11201068, 11671041) and “the Fundamental Research Funds for the Central Universities” in UIBE (Grant No. 14YQ07)

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Luan, N.N. Chung’s law of the iterated logarithm for subfractional Brownian motion. Acta. Math. Sin.-English Ser. 33, 839–850 (2017). https://doi.org/10.1007/s10114-016-6090-2

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  • DOI: https://doi.org/10.1007/s10114-016-6090-2

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