Local Strassen’s law of the iterated logarithm for increments of a Brownian motion in Hölder norm

Yonghong LIU, Weina WANG

Front. Math. China ›› 2025, Vol. 20 ›› Issue (2) : 91-98.

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PDF(386 KB)
Front. Math. China ›› 2025, Vol. 20 ›› Issue (2) : 91-98. DOI: 10.3868/s140-DDD-025-0008-x
RESEARCH ARTICLE

Local Strassen’s law of the iterated logarithm for increments of a Brownian motion in Hölder norm

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Abstract

With the help of large deviation of Brownian motion in the Hölder norm, local Strassen’s law of the iterated logarithm for increments of a Brownian motion in the Hölder norm is investigated. This paper promotes the corresponding results by Gantert and Wei.

Keywords

Brownian motion / increments / local Strassen’s law of the iterated logarithm / Hölder norm

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Yonghong LIU, Weina WANG. Local Strassen’s law of the iterated logarithm for increments of a Brownian motion in Hölder norm. Front. Math. China, 2025, 20(2): 91‒98 https://doi.org/10.3868/s140-DDD-025-0008-x

References

[1]
Baldi P., Ben Arous, G. , Kerkyacharian, G.. Large deviations and the Strassen theorem in Hölder norm. Stochastic Process Appl. 1992; 42(1): 171–180
[2]
Baldi P. , Roynette, B.. Some exact equivalents for the Brownian motion in Hölder norm. Probab. Theory Related Fields 1992; 93(4): 457–484
[3]
Gantert N.. An inversion of Strassen’s law of the iterated logarithm for small time. Ann. Probab. 1993; 21(2): 1045–1049
[4]
Gao F.Q. , Wang, Q.H.. The rate of convergence in the functional limit theorem for increments of a Brownian motion. Statist. Probab. Lett. 2005; 73(2): 165–177
[5]
Liu Y.H., Li, L.Q. , Wan, C.G.. The rate of convergence for increments of a Brownian motion in the Hölder norm. Statist. Probab. Lett. 2009; 79(12): 1463–1472
[6]
Wei Q.C.. Functional modulus of continuity for Brownian motion in the Hölder norm. Chinese Ann. Math. Ser. B 2001; 22(2): 223–232
[7]
Wei Q.C.. Functional limit theorems for C-R increments of k-dimensional Brownian motion in the Hölder norm. Acta Math. Sin. (Chin. Ser.) 2002; 45(1): 117–126

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