Fluctuation analysis for a class of nonlinear systems with fast periodic sampling and small state-dependent white noise

We consider a nonlinear differential equation under the combined influence of small state-dependent Brownian perturbations size ε, and fast periodic sampling with period δ; 0<ε,δ≪1. State samples (measurements) are taken every δ time units, instantaneous rate change state depends on both current value most recent sample. For resulting stochastic process indexed by ε,δ, we obtain asymptotic approximations for mean behavior fluctuations about mean. The former is described an ordinary equation, while latter governed (sde). This sde varies depending exact rates at which ε,δ↘0. key contribution involves computing effective drift term capturing interplay between noise in limiting sde. Connections control systems discussed illustrated numerically through simple example.