We develop a new approach for proving large deviation results for martingal
es based on a change of probability measure. It extends to the case of mart
ingales the conjugate distribution technique due to Cramer. To demonstrate
our approach, we derive formulae for probabilities of large deviations for
martingales with bounded jumps and bounded norming factor. Surprisingly eno
ugh, our result shows that the relative error in the normal range is of the
same order as in the case of sums of independent random variables. It also
allows to extend the range beyond the normal one. (C) 2000 Elsevier Scienc
e B.V. All rights reserved.