On Decomposition of the Last Passage Time of Diffusions

Masahiko Egami; Rusudan Kevkhishvili

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arXiv · 2210.01321

On Decomposition of the Last Passage Time of Diffusions

Masahiko Egami·Rusudan Kevkhishvili

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Abstract

For a regular transient diffusion, we provide a decomposition of its last passage time to a certain state $\alpha$. This is accomplished by transforming the original diffusion into two diffusions using the occupation time of the area above and below $\alpha$. Based on these two processes, both having a reflecting boundary at $\alpha$, we derive the decomposition formula of the Laplace transform of the last passage time explicitly in a simple form in terms of Green functions. This equation also leads to the Green function's decomposition formula. We demonstrate an application of these formulas to a diffusion with two-valued parameters.

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Masahiko Egami, Rusudan Kevkhishvili. 2022-10-04. On Decomposition of the Last Passage Time of Diffusions. https://arxiv.org/abs/2210.01321

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