Boyarski, Abraham; Góra, Pawełl A description of stochastic systems using chaotic maps. (English) Zbl 1071.37006 J. Appl. Math. Stochastic Anal. 2004, No. 2, 137-141 (2004). 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. Reviewer: Alexander Kachurovskij (Novosibirsk) Cited in 1 Document MSC: 37A50 Dynamical systems and their relations with probability theory and stochastic processes 60G05 Foundations of stochastic processes 28D05 Measure-preserving transformations Keywords:inverse Perron-Frobenius problem; invariant probability density functions; diffusion equation; chaotic maps PDFBibTeX XMLCite \textit{A. Boyarski} and \textit{P. Góra}, J. Appl. Math. Stochastic Anal. 2004, No. 2, 137--141 (2004; Zbl 1071.37006) Full Text: DOI EuDML