Random ODE and application to statistics
نویسنده
چکیده
Random ODE and application to statistics. Michail Zak Senior Research Scientist (Emeritus) Jet Propulsion Laboratory California Institute of Technology Pasadena, CA 91109 Abstract. It is demonstrated that any statistics can be represented by an attractor of the solution to the corresponding system of ODE coupled with its Liouville equation. Such a non-Newtonian representation allows one to reduce foundations of statistics to better-established foundations of ODE. In addition to that, evolution to the attractor reveals possible micro-mechanisms driving random events to the final distribution of the corresponding statistical law. Special attention is concentrated upon the power law and its dynamical interpretation: it is demonstrated that the underlying dynamics supports a “violent reputation” of the powerlaw statistics. As preliminary information, a review of origin of randomness in physics including new class of random ODE is presented.
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