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

TL;DR

This paper develops efficient algorithms for the exact sampling of the first passage time of a stable subordinator across a barrier, achieving complexity that depends logarithmically on the stability index.

Contribution

The paper introduces three novel algorithms for exact sampling of the first passage of a stable subordinator, avoiding numerical inversion or integration.

Findings

Algorithms achieve complexity O(1+|ln(1-α)|)

Sampling reduces to a bivariate distribution with parameters α and z

Exact sampling is feasible across different parameter regions

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 $O(1+|\ln(1-\alpha)|)$.