A description of stochastic systems using chaotic maps

[摘要] Letρ(x,t)denote a family of probability density functions parameterized by timet. We show the existence of a family{τ1:t>0}of deterministic nonlinear (chaotic) point transformations whose invariant probability density functions are preciselyρ(x,t). In particular, we are interested in the densities that arise from the diffusions. We derive a partial differential equation whose solution yields the family of chaotic maps whose density functions are precisely those of the diffusion.

[学科分类] 应用数学