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We present a hierarchical traversal algorithm for stochastic rasterization of motion blur, which efficiently reduces the number of inside tests needed to resolve spatio-temporal visibility. Our method is based on novel tile against moving primitive tests that also provide temporal bounds for the overlap. The algorithm works entirely in homogeneous coordinates, supports MSAA, facilitates efficient hierarchical spatio-temporal occlusion culling, and handles typical game workloads with widely varying triangle sizes. Furthermore, we use high-quality sampling patterns based on digital nets, and present a novel reordering that allows efficient procedural generation with good anti-aliasing properties. Finally, we evaluate a set of hierarchical motion blur rasterization algorithms in terms of both depth buffer bandwidth, shading efficiency, and arithmetic complexity.