# American Institute of Mathematical Sciences

March  2016, 9(1): 217-235. doi: 10.3934/krm.2016.9.217

## A random cloud model for the Wigner equation

 1 Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39 - 10117 Berlin

Received  December 2014 Revised  July 2015 Published  October 2015

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.
Citation: Wolfgang Wagner. A random cloud model for the Wigner equation. Kinetic & Related Models, 2016, 9 (1) : 217-235. doi: 10.3934/krm.2016.9.217
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