On the Joint Distribution of First-passage Time and First-passage Area of Drifted Brownian Motion

Mario Abundo () and Danilo Del Vescovo
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Mario Abundo: Università “Tor Vergata”, via della Ricerca Scientifica
Danilo Del Vescovo: Università “Tor Vergata”, via della Ricerca Scientifica

Methodology and Computing in Applied Probability, 2017, vol. 19, issue 3, 985-996

Abstract: Abstract For drifted Brownian motion X(t) = x-µ t + B t (µ > 0) starting from x > 0, we study the joint distribution of the first-passage time below zero ,t(x), and the first-passage area ,A(x), swept out by X till the time t(x). In particular, we establish differential equations with boundary conditions for the joint moments E[t(x) m A(x) n ], and we present an algorithm to find recursively them, for any m and n. Finally, the expected value of the time average of X till the time t(x) is obtained.

Keywords: First-passage time; First-passage area; One-dimensional diffusion; 60J60; 60H05; 60H10 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s11009-017-9546-7

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