IJPAM: Volume 30, No. 1 (2006)

THE ARC-SINE LAW FOR THE FIRST INSTANT
AT WHICH A DIFFUSION PROCESS EQUALS
THE ULTIMATE VALUE OF A FUNCTIONAL

Mario Abundo
Dipartimento di Matematica
Università ``Tor Vergata''
Via della Ricerca Scientifica, 00133 Roma, ITALY
e-mail: abundo@mat.uniroma2.it


Abstract.We study the distribution of the first instant $ \theta$ at which a diffusion process equals the ultimate value of a functional, showing that $ \theta$ follows a compound arc-sine law.

Received: May 15, 2006

AMS Subject Classification: 60J60, 60H05, 60H10

Key Words and Phrases: diffusion process, Brownian motion, stopping time, random time-change

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 30
Issue: 1