  Azuma's inequality is a tool for proving concentration bounds on random
variables. The inequality can be thought of as a natural generalization of
additive Chernoff bounds. On the other hand, the analogous generalization of
multiplicative Chernoff bounds has, to our knowledge, never been explicitly
formulated.
  We formulate a multiplicative-error version of Azuma's inequality. We then
show how to apply this new inequality in order to greatly simplify (and
correct) the analysis of contention delays in multithreaded systems managed by
randomized work stealing.
