Fast calculation of boundary crossing probabilities for Poisson processes

TL;DR

This paper introduces a fast algorithm with $O(n^2 \, \log n)$ complexity for calculating boundary crossing probabilities of Poisson processes, which are important in various applications.

Contribution

The paper presents a novel efficient algorithm for computing boundary crossing probabilities of Poisson processes with arbitrary boundaries.

Findings

Algorithm achieves $O(n^2 \log n)$ computational complexity.

Applicable to arbitrary upper and lower boundaries.

Significantly faster than previous methods.

Abstract

The boundary crossing probability of a Poisson process with $n$ jumps is a fundamental quantity with numerous applications. We present a fast $O(n^2 \log n)$ algorithm to calculate this probability for arbitrary upper and lower boundaries.