Approximation and convergence in the estimation of random parameters in linear holomorphic semigroups generated by regularly dissipative operators

We develop an abstract approximation and convergence framework for the estimation of random parameters in infinite dimensional dynamical systems governed by regularly dissipative operators in a Gelfand triple setting. Our results are motivated by a problem involving the development of a data analysis system for a transdermal alcohol biosensor. Our approach combines some recent results for random abstract parabolic systems with ideas contained in a treatment of Prohorov metric convergence of approximations in the estimation of random parameters in abstract dynamical systems based on aggregate or population data. Our approach differs in that we found it necessary to require that the distributions of our random parameters be described by probability density functions. Our convergence results rely on the well-known Trotter-Kato approximation theorem from linear semigroup theory.