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

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

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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