  We present a tractable non-independent increment process which provides a
high modeling flexibility. The process lies on an extension of the so-called
Harris chains to continuous time being stationary and Feller. We exhibit
constructions, properties, and inference methods for the process. Afterwards,
we use the process to propose a stochastic volatility model with an arbitrary
but fixed invariant distribution, which can be tailored to fit different
applied scenarios. We study the model performance through simulation while
illustrating its use in practice with empirical work. The model proves to be an
interesting competitor to a number of short-range stochastic volatility models.
