Theoretical analysis demonstrates an order n−1/2 convergence rate in random walks conditioned to stay positive, establishing sharp Berry–Esseen bounds under finite third moments.
We consider random walks conditioned to stay positive. When the mean of increments is zero and variance is finite it is known that their distribution converges to the Rayleigh law. In the present paper we derive a Berry–Esseen type estimate and show that if the third absolute moment is finite then the rate of convergence is of order n−1/2.
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Denisov et al. (2026) studied this question.
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