Brown单增量的局部泛函重对数律

刘永宏, 张晴晴

数学学报 ›› 2022, Vol. 65 ›› Issue (6) : 1083-1092.

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PDF(339 KB)
数学学报 ›› 2022, Vol. 65 ›› Issue (6) : 1083-1092. DOI: 10.12386/A20190074
论文

Brown单增量的局部泛函重对数律

    刘永宏, 张晴晴
作者信息 +

Local Functional Law of the Iterated Logarithm for Increments of a Brownian Sheet

    Yong Hong LIU, Qing Qing ZHANG
Author information +
文章历史 +

摘要

本文利用Brown单与Brown单增量的大偏差,得到了Brown单与Brown单增量的局部泛函重对数律.

Abstract

In this paper, using large deviations for a Brownian sheet and increments of a Brownian sheet, we obtain local functional law of the iterated logarithm for a Brownian sheet and increments of a Brownian sheet.

关键词

Brown单 / 增量 / 局部泛函重对数律

Key words

Brownian sheet / increments / local functional law of the iterated logarithm

引用本文

导出引用
刘永宏, 张晴晴. Brown单增量的局部泛函重对数律. 数学学报, 2022, 65(6): 1083-1092 https://doi.org/10.12386/A20190074
Yong Hong LIU, Qing Qing ZHANG. Local Functional Law of the Iterated Logarithm for Increments of a Brownian Sheet. Acta Mathematica Sinica, Chinese Series, 2022, 65(6): 1083-1092 https://doi.org/10.12386/A20190074

参考文献

[1] Gao F. Q., The Functional Lévy’s modulus for a multiparameter Wiener process (in Chinese), J. Hubei Univ. Nat. Sci., 1998, 20(4): 321–324.
[2] Kuelbs J., Li W. V., Small ball estimates for Brownian motion and the Brownian sheet, J. Theoret. Probab., 1993, 6(3): 547–577.
[3] Wang W. S., On Strassen-type theorem for the increments of two-parameter Wiener processes (in Chinese), Chin. Ann. Math., 2001, 22A(1): 27–34.
[4] Xu J. C., Quasi sure functional modulus of continuity for a two-parameter Wiener process in Hölder norm, J. Math. Anal. Appl., 2016, 34: 501–515.
[5] Xu J., Miao Y., Liu J., Quasi sure functional limit theorem for increments of a fractional Brownian sheet in Hölder norm, Communications in Statistics Theory and Methods, 2016, 45(5): 1564–1574.

基金

国家自然科学基金资助项目(11661025);广西自然科学基金(2020GXNSFAA159118);桂林电子科技大学数学与计算科学学院研究生创新项目(2022YJSCX04,2021YJSCX05)
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