Exponential Bounds in the Law of Iterated Logarithm for Martingales
  In this paper non-asymptotic exponential estimates are derived for tail of maximum martingale distribution by naturally norming in the spirit of the classical Law of Iterated Logarithm.   Key words: Martingales, exponential estimations, moment, Banach spaces of random variables, tail of distribution, conditional expectation. 
E. Ostrovsky, L.Sirota