Nonlinear statistical coupling |
| |
Authors: | Kenric P Nelson Sabir Umarov |
| |
Institution: | a Raytheon Company, Woburn, MA 01801, USA b Department of Mathematics, Tufts University, Medford, MA 02155, USA |
| |
Abstract: | By considering a nonlinear combination of the probabilities of a system, a physical interpretation of Tsallis statistics as representing the nonlinear coupling or decoupling of statistical states is proposed. The escort probability is interpreted as the coupled probability, with Q=1−q defined as the degree of nonlinear coupling between the statistical states. Positive values of Q have coupled statistical states, a larger entropy metric, and a maximum coupled-entropy distribution of compact-support coupled-Gaussians. Negative values of Q have decoupled statistical states and for −2<Q<0 a maximum coupled-entropy distribution of heavy-tail coupled-Gaussians. The conjugate transformation between the heavy-tail and compact-support domains is shown to be for coupled-Gaussian distributions. This conjugate relationship has been used to extend the generalized Fourier transform to the compact-support domain and to define a scale-invariant correlation structure with heavy-tail limit distribution. In the present paper, we show that the conjugate is a mapping between the source of nonlinearity in non-stationary stochastic processes and the nonlinear coupling which defines the coupled-Gaussian limit distribution. The effects of additive and multiplicative noise are shown to be separable into the coupled-variance and the coupling parameter Q, providing further evidence of the importance of the generalized moments. |
| |
Keywords: | Nonlinear coupling _method=retrieve& _eid=1-s2 0-S0378437110000993& _mathId=si29 gif& _pii=S0378437110000993& _issn=03784371& _acct=C000069490& _version=1& _userid=6211566& md5=797e656b5a7c3ded33f42b87c53f5dad')" style="cursor:pointer q-Gaussian" target="_blank">" alt="Click to view the MathML source" title="Click to view the MathML source">q-Gaussian _method=retrieve& _eid=1-s2 0-S0378437110000993& _mathId=si30 gif& _pii=S0378437110000993& _issn=03784371& _acct=C000069490& _version=1& _userid=6211566& md5=b38692d1913fd270e5582d1832817f44')" style="cursor:pointer q-statistics" target="_blank">" alt="Click to view the MathML source" title="Click to view the MathML source">q-statistics Multiplicative noise Non-stationary stochastic processes |
本文献已被 ScienceDirect 等数据库收录! |
|