Brown运动增量在Hölder范数下的局部泛函Chung重对数律

刘永宏, 王为娜

数学学报 ›› 2019, Vol. 62 ›› Issue (4) : 605-612.

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数学学报 ›› 2019, Vol. 62 ›› Issue (4) : 605-612. DOI: 10.12386/A2019sxxb0056
论文

Brown运动增量在Hölder范数下的局部泛函Chung重对数律

    刘永宏, 王为娜
作者信息 +

Local Functional Chung's Law of the Iterated Logarithm for Increments of a Brownian Motion in Hölder Norm

    Yong Hong LIU, Wei Na WANG
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摘要

本文利用Brown运动在Hölder范数下的大偏差和小偏差,得到了Brown运动增量在Hölder范数下的局部泛函Chung重对数律.

Abstract

Using large deviation and small deviation of Brownian motion in Hölder norm, local functional Chung's law of the iterated logarithm for increments of a Brownian motion in Hölder norm can be obtained.

关键词

Brown运动 / 增量 / 局部泛函Chung重对数律 / / lder范数

Key words

Brownian motion / increments / local functional Chung's law of the iterated logarithm / Hölder norm

引用本文

导出引用
刘永宏, 王为娜. Brown运动增量在Hölder范数下的局部泛函Chung重对数律. 数学学报, 2019, 62(4): 605-612 https://doi.org/10.12386/A2019sxxb0056
Yong Hong LIU, Wei Na WANG. Local Functional Chung's Law of the Iterated Logarithm for Increments of a Brownian Motion in Hölder Norm. Acta Mathematica Sinica, Chinese Series, 2019, 62(4): 605-612 https://doi.org/10.12386/A2019sxxb0056

参考文献

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[3] Baldi P., Roynette B., Some exact equivalents for the Brownian motion in Hölder norm, Probab. Theory Relat. Fields, 1992, 93:457-484.
[4] Gao F., Wang Q., The rate of convergence in the functional limit theorem for increments of a Brownian motion, Statist. & Probab. Lett., 2005, 73:165-177.
[5] Liu Y., Li L., Wan C., The rate of convergence for increments of a Brownian motion in Hölder norm, Statist. & Probab. Lett., 2009, 79:1463-1472.
[6] Lucas A., Fractales aléatoires de type Chung pour les accroissements du processus de Wiener, C. R. Acad. Sci. Paris, Ser. I, 1998, 326:1123-1126.
[7] Lucas A., Thilly E., Loi de type Chung en norme de Hölder pour les accroissements locaux du mouvement Brownien. C. R. Acad. Sci. Paris, Ser. I, 2003, 336:1029-1032.
[8] Wei Q., Functional modulus of continuity for Brownian motion in Hölder norm, Chin. Ann. of Math., 2001, 22B(2):223-232.

基金

国家自然科学基金资助项目(11661025)

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