Trapping for Newtonian Diffusion Processes

  • Ph. Blanchard
Conference paper
Part of the Acta Physica Austriaca book series (FEWBODY, volume 26/1984)


In the first lecture I will try to explain a general mechanism for the formation of impenetrable barriers for diffusion processes (see [1]). I will consider a special class of diffusion processes, which we call Newtonian diffusions. This name is justified by the fact that such a diffusion process satisfies a Newton law in the mean. We will see how it is possible to define a mean stochastic acceleration a for diffusion processes. The Newton law in the mean
$$\mu a\, = \,F\, = \, - \nabla \nabla$$
where µ is the mass of a test-particle, plays the role of a constraint and allows to construct under some assumptions a family of possible probability distributions ρ of the stochastic diffusion process. We will also show that the nodal surfaces of \(N_\rho \, = \,\left\{ {x\, \in \,R^d |\rho \,(t,x)\, = \,0} \right\}\) can also be impenetrable barriers, splitting the family of typical particles into several groups. Since no particle can pass from one group to another we have to do with a segregation (confinement, trapping) mechanism.


Diffusion Process Stochastic Differential Equation Central Body Dirichlet Form Radiation Belt 
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Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • Ph. Blanchard
    • 1
  1. 1.Theoretische Physik and BiBoSUniversität BielefeldBielefeld 1Germany

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