  We study a nonparametric Bayesian approach to estimation of the volatility
function of a stochastic differential equation driven by a gamma process. The
volatility function is modelled a priori as piecewise constant, and we specify
a gamma prior on its values. This leads to a straightforward procedure for
posterior inference via an MCMC procedure. We give theoretical performance
guarantees (contraction rates for the posterior) for the Bayesian estimate in
terms of the regularity of the unknown volatility function. We illustrate the
method on synthetic and real data examples.
