Equations of identifiability of nonlinear parametric stochastic systems (Q1095102)

The paper contains an extension of the results of the author's earlier papers [Avtom. Telemekh. 1985, No.5, 64-78 (1985; Zbl 0601.93058); ibid., No.7, 96-109 (1985; Zbl 0612.93066)] to stochastic systems that are nonlinear in the parameters and the variables. A class of systems whose operators are nonlinear transformations of forms that are linear in the parameters and nonlinear in the variables is considered. It is proved that the nonlinear system under consideration has a unique parametric description if and only if the parametric description of all its forms that are linear in the parameters is unique. Owing to this the analysis of the identifiability of systems that are nonlinear in the parameters and the variables is reduced to an analysis of the identifiability of systems that are linear in the parameters. The obtained results yield a condition of global identifiability of the considered nonlinear systems, and they do not involve linearization of nonlinear systems.