In this paper, we consider a unidimensional piecewise deterministic Markov process (PDMP), with homogeneous jump rate $\mathit{\lambda }(\mathit{x})$. 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 ${\hat{\mathit{\lambda }}}_{\mathit{n}}$ 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 ${ln}^2(\mathit{n})$ factor). The simulations illustrate our theoretical results.