A sufficient condition is given such that the marginal conditional p.d.f. of an n-dimensional diffusion process (n > 1) originating at an assigned point in the diffusion region reduces to the transition p.d.f. of a one-dimensional diffusion process. Under such condition, the first-passage-time p.d.f. through a curve in the diffusion region can be seen to identify with the first-passage-time p.d.f. for a one-dimensional diffusion process through a suitable boundary. The first-passage-time p.d.f. through either of two curves for the n-dimensional process is then also reduced to a first-passage-time p.d.f. for a one-dimensional diffusion process through a pair of suitable boundaries.
On the reduction to one dimension of first-passage-time problems for diffusion processes / A., DI CRESCENZO; V., Giorno; A. G., Nobile; Ricciardi, LUIGI MARIA. - In: JOURNAL OF MATHEMATICAL AND PHYSICAL SCIENCES. - ISSN 0047-2557. - STAMPA. - 25:6(1991), pp. 599-611.
On the reduction to one dimension of first-passage-time problems for diffusion processes
RICCIARDI, LUIGI MARIA
1991
Abstract
A sufficient condition is given such that the marginal conditional p.d.f. of an n-dimensional diffusion process (n > 1) originating at an assigned point in the diffusion region reduces to the transition p.d.f. of a one-dimensional diffusion process. Under such condition, the first-passage-time p.d.f. through a curve in the diffusion region can be seen to identify with the first-passage-time p.d.f. for a one-dimensional diffusion process through a suitable boundary. The first-passage-time p.d.f. through either of two curves for the n-dimensional process is then also reduced to a first-passage-time p.d.f. for a one-dimensional diffusion process through a pair of suitable boundaries.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.