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%2C a family of non-diffusive stochastic processes consisting of deterministic motion and random jumps at random times. Similarly to diffusions%2C such Markov processes admit time reversals that turn out to be PDMPs as well. We apply this observation to three PDMPs considered in the literature: the Zig-Zag process%2C Bouncy Particle Sampler%2C and Randomised Hamiltonian Monte Carlo. For these three particular instances%2C we show that the jump rates and kernels of the corresponding time reversals admit explicit expressions depending on some conditional densities of the PDMP under consideration before and after a jump. Based on these results%2C we propose efficient training procedures to learn these characteristics and consider methods to approximately simulate the reverse process. Finally%2C we provide bounds in the total variation distance between the data distribution and the resulting distribution of our model in the case where the base distribution is the standard %24d%24-dimensional Gaussian distribution. Promising numerical simulations support further investigations into this class of models.?quality=80&w=800)
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