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Some liminf results on increments of the primitives of Brownian motion

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Abstract

Let {W(t); t≥0} be a standard Brownian motion. For a positive integer m, define a Gaussian process

$$X_m \left( t \right) = \frac{1}{{m!}}\int_0^t { \left( {t - s} \right)^m dW\left( s \right)} $$

. In this paper the liminf behavior of the increments of this process is discussed by establishing some probability inequalities. Some previous results are extended and improved.

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Authors and Affiliations

  1. Dept. of Math., Hangzhou Teachers’ College, 310012, Hangzhou

    Wang Wensheng

Authors
  1. Wang Wensheng
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Project Supported by National Science Fundation of China (19571021) and Zhejiang Province.

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Wensheng, W. Some liminf results on increments of the primitives of Brownian motion. Appl. Math. Chin. Univ. 15, 409–418 (2000). https://doi.org/10.1007/s11766-000-0038-z

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  • DOI: https://doi.org/10.1007/s11766-000-0038-z

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