WIAS Preprint No. 2083, (2015)

A random cloud model for the Wigner equation


  • Wagner, Wolfgang

2010 Mathematics Subject Classification

  • 60J25 81Q05


  • Wigner equation, probabilistic representation, stochastic particle model, piecewise deterministic Markov process




A probabilistic model for the Wigner equation is studied. The model is based on a particle system with the time evolution of a piecewise deterministic Markov process. Each particle is characterized by a real-valued weight, a position and a wave-vector. The particle position changes continuously, according to the velocity determined by the wave-vector. New particles are created randomly and added to the system. The main result is that appropriate functionals of the process satisfy a weak form of the Wigner equation.

Appeared in

  • Kinet. Relat. Models, 9 (2016) pp. 217--235.

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