Some asymptotic results related to the law of iterated logarithm for Brownian motion

1995 ◽  
Vol 8 (3) ◽  
pp. 643-667 ◽  
Author(s):  
Terence Chan
Keyword(s):  
Brownian Motion ◽  
Law Of Iterated Logarithm ◽  
Asymptotic Results ◽  
Iterated Logarithm ◽  
The Law

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.

Some asymptotic results for exponential functionals of Brownian motion

1995 ◽  
Vol 32 (4) ◽  
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.

The Law of Iterated Logarithm

1994 ◽  
pp. 443-460
Author(s):  
V. S. Koroljuk ◽  
Yu. V. Borovskich
Keyword(s):  
Law Of Iterated Logarithm ◽  
Iterated Logarithm ◽  
The Law
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