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

Mario Abundo
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Mario Abundo: Dipartimento di Matematica, Università Tor Vergata, 00133 Rome, Italy

Mathematics, 2018, vol. 6, issue 6, 1-10

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.

Keywords: first-passage time; inverse first-passage problem; diffusion (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
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