  Limit distributions for the greatest convex minorant and its derivative are
considered for a general class of stochastic processes including partial sum
processes and empirical processes, for independent, weakly dependent and long
range dependent data. The results are applied to isotonic regression, isotonic
regression after kernel smoothing, estimation of convex regression functions,
and estimation of monotone and convex density functions. Various pointwise
limit distributions are obtained, and the rate of convergence depends on the
self similarity properties and on the rate of convergence of the processes
considered.
