  We present a survey of some of our recent results on Bayesian nonparametric
inference for a multitude of stochastic processes. The common feature is that
the prior distribution in the cases considered is on suitable sets of piecewise
constant or piecewise linear functions, that differ for the specific situations
at hand. Posterior consistency and in most cases contraction rates for the
estimators are presented. Numerical studies on simulated and real data
accompany the theoretical results.
