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arXiv · 2506.03047

Complexity of exact sampling of the first passage of a stable subordinator

Zhiyi Chi
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Abstract

We consider the exact sampling of the first passage of a stable subordinator across a non-increasing regular barrier. First, the sampling is reduced to one from a bivariate distribution parameterized by the index $\alpha$ of the subordinator and a scalar $z$ independent of the barrier. Then three algorithms are devised for different regions of $(\alpha, z)$, using the acceptance-rejection method without numerical inversion or integration. When combined, the algorithms allow the exact sampling of the first passage to be done with complexity $O(1+|\ln(1-\alpha)|)$.

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Zhiyi Chi. 2025-06-03. Complexity of exact sampling of the first passage of a stable subordinator. https://arxiv.org/abs/2506.03047

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