Piecewise-deterministic Markov processes offer a wide range of stochastic spatial dynamical models. Their behavior is governed by an ordinary differential equation punctuated by random jumps occuring at random times. We focus on the nonparametric estimation problem of the jump rate for such a stochastic model observed within a long time interval. I will present two strategies for estimating this feature of the process: the first one relies on the multiplicative intensity model and does not require to know the explicit form of the deterministic flow; from the second strategy, based on recursive kernel methods, we construct a family of consistent estimators among which we choose the one with minimal variance.

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