A distribution F on (-∞, ∞) is said to belong to the class S(γ) for some γ ≥ 0 if ${\rm lim}_{x\rightarrow \infty}\overline{F}(x-u)/\overline{F}(x)={\rm e ...
We establish a correspondence between the limit distribution and the asymptotic entropy of random walks on ℤ, which have a sequence of step length that is exponentially increasing up to some error, ...
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