On Decomposition of the Last Passage Time of Diffusions

Fuente: arXiv
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Autori principali: Egami, Masahiko, Kevkhishvili, Rusudan
Natura: Preprint
Pubblicazione: 2022
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author Egami, Masahiko
Kevkhishvili, Rusudan
author_facet Egami, Masahiko
Kevkhishvili, Rusudan
contents For a regular transient diffusion, we provide a decomposition of its last passage time to a certain state $α$. This is accomplished by transforming the original diffusion into two diffusions using the occupation time of the area above and below $α$. Based on these two processes, both having a reflecting boundary at $α$, 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.
format Preprint
id arxiv_https___arxiv_org_abs_2210_01321
institution arXiv
publishDate 2022
record_format arxiv
spellingShingle On Decomposition of the Last Passage Time of Diffusions
Egami, Masahiko
Kevkhishvili, Rusudan
Probability
60J60
For a regular transient diffusion, we provide a decomposition of its last passage time to a certain state $α$. This is accomplished by transforming the original diffusion into two diffusions using the occupation time of the area above and below $α$. Based on these two processes, both having a reflecting boundary at $α$, 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.
title On Decomposition of the Last Passage Time of Diffusions
topic Probability
60J60
url https://arxiv.org/abs/2210.01321