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A description of stochastic systems using chaotic maps. (English) Zbl 1071.37006

Authors’ abstract: Let \(\rho(x, t)\) denote a family of probability density functions parameterized by time \(t\). We show the existence of a family \(\{\tau_t: t> 0\}\) of deterministic nonlinear (chaotic) point transformations whose invariant probability density functions are precisely \(\rho(x,t)\). In particular, we are interested in densities that arise from diffusions. We derive a partial differential equation whose solution yields the family of chaotic maps whose density functions are precisely those of the diffusion.

MSC:

37A50 Dynamical systems and their relations with probability theory and stochastic processes
60G05 Foundations of stochastic processes
28D05 Measure-preserving transformations
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