Confidence Bands for Evolution Systems Described by Parameter-Dependent Analytic Semigroups

We use the delta method and finite dimensional approximation to derive confidence bands for random parameter-dependent impulse response functions (IRF) and system outputs in the form of convolutions for evolution systems described by analytic semigroups of operators with regularly dissipative generators set in a Gelfand triple of Hilbert spaces. Central to our approach is the Fr ' echet derivative of the parameter-dependent analytic semigroup and the convergence of finite dimensional approximations to it. An example involving the biosensor measurement of transdermal alcohol resulting from blood alcohol is presented and numerical results are discussed.