Aperiodic random walks: uniform estimates, local limits and invariance principles
Jiaming Xu
Abstract
We prove uniform endpoint estimates, killed local limits, and conditioned-bridge invariance principles for triangular arrays of centered, aperiodic, integer-valued random walks with uni- form exponential tails. The endpoint estimates cover all nonnegative heights, while the local limits treat positive diffusive and zero endpoints. The increment law may vary with the scaling parameter.
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