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A central limit theorem for two-dimensional random walks in a cone. (Un théorème limite central pour des marches aléatoires dans des cônes du plan.) (English. French summary) Zbl 1217.60026
Summary: We prove that a planar random walk with bounded increments and mean zero which is conditioned to stay in a cone converges weakly to the corresponding Brownian meander if and only if the tail distribution of the exit time from the cone is regularly varying. This condition is satisfied in many natural examples.

MSC:
60F17 Functional limit theorems; invariance principles
60G50 Sums of independent random variables; random walks
60J05 Discrete-time Markov processes on general state spaces
60J65 Brownian motion
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