The randomized first-hitting problem of continuously time-changed Brownian motion
type: Item
instance of: scholarly article
title: The randomized first-hitting problem of continuously time-changed Brownian motion
zbMATH Open document ID: 1426.60107
author: Mario Abundo
published in: Mathematics
publication date: 2018-12-18T00:00:00Z
review text: Summary: Let \(X(t)\) be a continuously time-changed Brownian motion starting from a random position \(\eta\), \(S(t)\) a given continuous, increasing boundary, with \(S(0) \geq 0\), \(P(\eta \geq S(0)) = 1\), and \(F\) an assigned distribution function. We study the inverse first-passage time problem for \(X(t)\), which consists in finding the distribution of \(\eta\) such that the first-passage time of \(X(t)\) below \(S(t)\) has distribution \(F\), generalizing the results, valid in the case when \(S(t)\) is a straight line. Some explicit examples are reported.
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 60J60
zbMATH DE Number: 6994622
zbMATH Keywords: first-passage time
zbMATH Keywords: inverse first-passage problem
zbMATH Keywords: diffusion
MaRDI profile type: Publication
full work available at URL: math6060091
OpenAlex ID: W2806293959
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Wikidata QID: Q129801897
DOI: 10.3390/MATH6060091
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description: scientific article; zbMATH DE number 6994622