Abstract
The asymptotic behavior of exponential statistical experiments set by the exponential symmetric statistics is studied. In this case, the property of a persistent linear regression, which means the dependence of separate results of the experiment on the averaging of previous experiments, is assumed. For the exponential statistical experiments in a scheme of series (as N → ∞), the equilibrium mode is established, and the approximation of the normal autoregression by an exponential process is constructed.
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