The problem of real-time photorealistic imaging of digital terrain is discussed. New technique for specifying digital terrain by scalar perturbation functions without its approximation by polygons is considered. A recursive algorithm for object space subdivision with masking of invisible surfaces and an effective technique of projective transformation for perspective imaging are proposed. The p...

We prove a law of the iterated logarithm for stable processes in a random scenery. The proof relies on the analysis of a new class of stochastic processes which exhibit long-range dependence.

We consider the question of when a random walk on a finite abelian group with a given step distribution can be used to reconstruct a binary labeling of the elements of the group, up to a shift. Matzinger and Lember (2006) give a sufficient condition for reconstructibility on cycles. While, as we show, this condition is not in general necessary, our main result is that it is necessary when the l...