The integral equations are exploited to determine the asymptotic behaviour of the first passage time (FPT) p.d.f.'s through certain time-varying boundaries, including periodic boundaries, for a class of one-dimensional diffusion processes possessing steady-state densities. Sufficient conditions for the FPT density to exhibit an asymptotically exponential behaviour are given. Explicit formulas for the Ornstein-Uhlenbeck process are obtained and some new asymptotic results for the FPT density of the Wiener process are proved.
On the asymptotics of first passage time densities
GIORNO, Virginia;NOBILE, Amelia Giuseppina
1990-01-01
Abstract
The integral equations are exploited to determine the asymptotic behaviour of the first passage time (FPT) p.d.f.'s through certain time-varying boundaries, including periodic boundaries, for a class of one-dimensional diffusion processes possessing steady-state densities. Sufficient conditions for the FPT density to exhibit an asymptotically exponential behaviour are given. Explicit formulas for the Ornstein-Uhlenbeck process are obtained and some new asymptotic results for the FPT density of the Wiener process are proved.File in questo prodotto:
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