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Limit Behavior of the "Horizontal-Vertical" Random Walk and Some Extensions of the Donsker-Prokhorov Invariance Principle
We consider a two-dimensional random walk that moves in the horizontal direction on the half-plane {y>x} and in the vertical direction on the half-plane $\{y\le x\}$. The limit behavior (as the time interval between two steps and the size of each step tend to zero) of this "horizontal-vertical" random walk …