In this paper, we consider a unidimensional piecewise deterministic Markov process (PDMP), with homogeneous jump rate λ(x) . This process is observed continuously, so the flow φ is known. To estimate nonparametrically the jump rate, we first construct an adaptive estimator of the stationary density, then we derive a quotient estimator λ n of λ. Under some ergodicity conditions, we bound the risk of these estimators (and give a uniform bound on a small class of functions), and prove that the estimator of the jump rate is nearly minimax (up to a ln 2 (n) factor). The simulations illustrate our theoretical results.