Exact targeting of gibbs distributions using velocity-jump processes

This work introduces and studies a new family of velocity jump Markov processes directly amenable to exact simulation with the following two properties: (i) trajectories converge in law, when time-step parameter vanishes, towards given Langevin or Hamiltonian dynamics; (ii) stationary distribution process is always exactly by product Gaussian (for velocities) any target log-density. The itself, addition computability gradient log-density, depends on knowledge appropriate explicit upper bounds lower order derivatives this does not exhibit reflections (maximum size jumps can be controlled) suitable for ’factorization method’. We provide rigorous mathematical proofs convergence Hamiltonian/Langevin dynamics time step exponentially fast noise velocities present. Numerical implementation detailed illustrated.