The law of the iterated logarithm for Brownian sheets

1975 ◽  
Vol 12 (4) ◽  
pp. 840-844
Author(s):  
W. J. Park
Keyword(s):  
Banach Space ◽  
Brownian Motion ◽  
Iterated Logarithm ◽  
The Law

Strassen-type law of the iterated logarithm for Brownian sheets presented by Pyke [7] is proved by using recent results of Kuelbs and Lepage [4]: the law of the iterated logarithm for Brownian motion in a Banach space and some applications are given.

The law of the iterated logarithm for Brownian sheets

1975 ◽  
Vol 12 (04) ◽  
pp. 840-844
Author(s):  
W. J. Park
Keyword(s):  
Banach Space ◽  
Brownian Motion ◽  
Iterated Logarithm ◽  
The Law

Strassen-type law of the iterated logarithm for Brownian sheets presented by Pyke [7] is proved by using recent results of Kuelbs and Lepage [4]: the law of the iterated logarithm for Brownian motion in a Banach space and some applications are given.

Some asymptotic results for exponential functionals of Brownian motion

1995 ◽  
Vol 32 (04) ◽  
pp. 930-940 ◽  
Author(s):  
J.-C. Gruet ◽  
Z. Shi
Keyword(s):  
Brownian Motion ◽  
Upper Class ◽  
Financial Mathematics ◽  
Asymptotic Results ◽  
Integral Test ◽  
Iterated Logarithm ◽  
Planar Brownian Motion ◽  
The Law ◽  
Straightforward Consequence

The study of exponential functionals of Brownian motion has recently attracted much attention, partly motivated by several problems in financial mathematics. Let be a linear Brownian motion starting from 0. Following Dufresne (1989), (1990), De Schepper and Goovaerts (1992) and De Schepper et al. (1992), we are interested in the process (for δ > 0), which stands for the discounted values of a continuous perpetuity payment. We characterize the upper class (in the sense of Paul Lévy) of X, as δ tends to zero, by an integral test. The law of the iterated logarithm is obtained as a straightforward consequence. The process exp(W(u))du is studied as well. The class of upper functions of Z is provided. An application to the lim inf behaviour of the winding clock of planar Brownian motion is presented.

scholarly journals On the law of the iterated logarithm for Brownian motion on compact manifolds

2019 ◽  
Vol 62 (8) ◽  
pp. 1511-1518
Author(s):  
Cheng Ouyang ◽  
Jennifer Pajda-De La O
Keyword(s):  
Brownian Motion ◽  
Compact Manifolds ◽  
Iterated Logarithm ◽  
The Law
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