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Mathematics 2018, 6(6), 91; https://doi.org/10.3390/math6060091

The Randomized First-Hitting Problem of Continuously Time-Changed Brownian Motion

Dipartimento di Matematica, Università Tor Vergata, 00133 Rome, Italy
Received: 4 April 2018 / Revised: 24 May 2018 / Accepted: 25 May 2018 / Published: 28 May 2018
(This article belongs to the Special Issue Stochastic Processes with Applications)
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Abstract

Let X ( t ) be a continuously time-changed Brownian motion starting from a random position η , S ( t ) a given continuous, increasing boundary, with S ( 0 ) 0 , P ( η 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 η 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. View Full-Text
Keywords: first-passage time; inverse first-passage problem; diffusion first-passage time; inverse first-passage problem; diffusion
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Abundo, M. The Randomized First-Hitting Problem of Continuously Time-Changed Brownian Motion. Mathematics 2018, 6, 91.

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