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Abstract
We consider a classical model related to an empirical distribution function of (ξ
k
)
i≥1 – i.i.d. sequence of random variables, supported on the interval [0, 1], with continuous distribution function
. Applying “Stopping Time Techniques”, we give a proof of Kolmogorov's exponential bound
conjectured by Kolmogorov in 1943. Using this bound we establish a best possible logarithmic asymptotic of
with rate
slower than
for any
.
Notes
Recommended by A. G. Tartakovsky