Fast calculation of boundary crossing probabilities for Poisson processes

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.

8 pages, 2 figures, associated C++ code is available at http://www.wisdom.weizmann.ac.il/~amitmo

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