Portal de Periódicos da CAPES

First-passage-time density and moments of the ornstein-uhlenbeck process

1988; Cambridge University Press; Volume: 25; Issue: 1 Linguagem: Inglês

10.2307/3214232

1475-6072

Luigi M. Ricciardi, Shunsuke Sato,

Diffusion and Search Dynamics

A detailed study of the asymptotic behavior of the first-passage-time p.d.f. and its moments is carried out for an unrestricted conditional Ornstein-Uhlenbeck process and for a constant boundary. Explicit expressions are determined which include those earlier discussed by Sato [15] and by Nobile et al. [9]. In particular, it is shown that the first-passage-time p.d.f. can be expressed as the sum of exponential functions with negative exponents and that the latter reduces to a single exponential density as time increases, irrespective of the chosen boundary. The explicit expressions obtained for the first-passage-time moments of any order appear to be particularly suitable for computation purposes.