  Cramer's theorem provides an estimate for the tail probability of the maximum
of a random walk with negative drift and increments having a moment generating
function finite in a neighborhood of the origin. The class of (g,F)-processes
generalizes in a natural way random walks and fractional ARIMA models used in
time series analysis. For those (g,F)-processes with negative drift, we obtain
a logarithmic estimate of the tail probability of their maximum, under
conditions comparable to Cramer's. Furthermore, we exhibit the most likely
paths as well as the most likely behavior of the innovations leading to a large
maximum.
