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Название: Escape of a Uniform Random Walk from an Interval
Авторы: Antal T., Redner S.
Journal of Statistical Physics, Vol. 123, No. 6, June 2006. p. 1129-1144.
We study the ﬁrst-passage properties of a random walk in the unit interval in which the length of a single step is uniformly distributed over the ﬁnite range [−a,a]. For a of the order of one, the exit probabilities to each edge of the interval and the exit time from the interval exhibit anomalous properties stemming from the change in the minimum number of steps to escape the interval as a function of the starting point. As a decreases, ﬁrst-passage properties approach those of continuum diffusion, but non-diffusive effects remain because of residual discreteness effects.