抄録
In this paper, we consider an identification problem for a nonstationary parameter contained in stochastic nonlinear dynamical systems, whose states are modeled by stochastic boundary value processes. We review nonlinear filtering problems for stochastic boundary processes where the unknown nonstationary parameter is fixed. An equation of an unnormalized conditional distribution for Xt (system state) given by Yt (observation) and θt (parameter) is derived.
Introducing a pathwise version of this equation, existence of maximum likelihood estimates (M.L.E.) for the unknown parameter θ. is studied. The consistency property for M.L.E. is also explored under many independent experimental observation data. In order to derive a realization algorithm for M.L.E., necessary conditions for an optimal M.L.E., i.e., variational inequality and adjoint equation are presented.
