  We provide quantitative bounds for the long time behavior of a class of
Piecewise Deterministic Markov Processes with state space Rd \times E where E
is a finite set. The continuous component evolves according to a smooth vector
field that switches at the jump times of the discrete coordinate. The jump
rates may depend on the whole position of the process. Under regularity
assumptions on the jump rates and stability conditions for the vector fields we
provide explicit exponential upper bounds for the convergence to equilibrium in
terms of Wasserstein distances. As an example, we obtain convergence results
for a stochastic version of the Morris-Lecar model of neurobiology.
