A central limit theorem for two-dimensional random walks in a cone

Details A central limit theorem for two-dimensional random walks in a cone A central limit theorem for two-dimensional random walks in a cone

2009-11-25

arxiv.org/abs/0911.4774v3

Mathematics

Probability

Scientific paper

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.

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