Reconstruction of Stochastic Processes Using Frames

Abstract

This note discusses sampling in a general context and shows that the (dual) frame reconstruction formula holds for stochastic processes, in quadratic mean. Specifically we show that if the covariance can be reconstructed using frames then the sample path can also be reconstructed. The application of the result for the generation of approximate sample paths for simulation is discussed. Ergodic properties of the approximate estimators are also investigated.