ISSN:
1572-9613
Keywords:
Maxima statistics
;
first-passage-time statistics
;
Wiener-Einstein processes
;
random walks
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract The maxima and first-passage-time statistics of Wiener-Einstein processes are evaluated analytically in one, two, and three dimensions. We show that the mean square maximum displacement has the same time dependence as the mean square displacement, i.e., it grows linearly with time. The ratio of the mean square maximum to the mean square displacement is shown to decrease with increasing dimensionality. We also calculate the mean first passage time for the process to attain a given absolute displacement and find that it grows as the square of the displacementand is independent of the dimensionality of the process. In addition, we evaluate the dispersion of maxima and of first passage times and discuss their dependence on dimensionality.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01007989
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