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We propose a scalable method for forward stochastic reachability analysis foruncontrolled linear systems with affine disturbance. Our method uses Fouriertransforms to efficiently compute the forward stochastic reach probabilitymeasure (density) and the forward stochastic reach set. This method isapplicable to systems with bounded or unbounded disturbance sets. We alsoexamine the convexity properties of the forward stochastic reach set and itsprobability density. Motivated by the problem of a robot attempting to capturea stochastically moving, non-adversarial target, we demonstrate our method ontwo simple examples. Where traditional approaches provide approximations, ourmethod provides exact analytical expressions for the densities and probabilityof capture.

Forward Stochastic Reachability Analysis for Uncontrolled Linear Systems using Fourier Transforms