The first-passage-time p.d.f. through a time-dependent boundary for one-dimensional diffusion processes is proved to satisfy a new Volterra integral equation of the second kind involving two arbitrary continuous functions. Use of this equation is made to prove that for the Wiener and the Ornstein-Uhlenbeck processes the singularity of the kernel can be removed by a suitable choice of these functions. A simple and efficient numerical procedure for the solution of the integral equation is provided and its convergence is briefly discussed. Use of this equation is finally made to obtain closed-form expressions for first-passage-time p.d.f.'s in the case of various time-dependent boundaries.
A new integral equation for the evaluation of first-passage-time probability densities / Buonocore, Aniello; A. G., Nobile; Ricciardi, LUIGI MARIA. - In: ADVANCES IN APPLIED PROBABILITY. - ISSN 0001-8678. - STAMPA. - 19:4(1987), pp. 784-800. [10.2307/1427102]
A new integral equation for the evaluation of first-passage-time probability densities
BUONOCORE, ANIELLO;RICCIARDI, LUIGI MARIA
1987
Abstract
The first-passage-time p.d.f. through a time-dependent boundary for one-dimensional diffusion processes is proved to satisfy a new Volterra integral equation of the second kind involving two arbitrary continuous functions. Use of this equation is made to prove that for the Wiener and the Ornstein-Uhlenbeck processes the singularity of the kernel can be removed by a suitable choice of these functions. A simple and efficient numerical procedure for the solution of the integral equation is provided and its convergence is briefly discussed. Use of this equation is finally made to obtain closed-form expressions for first-passage-time p.d.f.'s in the case of various time-dependent boundaries.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.