We prove that for a diffusion process the first-passage-time p.d.f. through a continuous-time function with bounded derivative satisfies a Volterra integral equation of the second kind whose kernel and right-hand term are probability currents. For the case of the standard Wiener process this equation is solved in closed form not only for the class of boundaries already introduced by Park and Paranjape [15] but also for other boundaries for which no explicit analytical results have previously been available.

On an integral equation for first passage time probability density function.

SACERDOTE, Laura Lea;
1984

Abstract

We prove that for a diffusion process the first-passage-time p.d.f. through a continuous-time function with bounded derivative satisfies a Volterra integral equation of the second kind whose kernel and right-hand term are probability currents. For the case of the standard Wiener process this equation is solved in closed form not only for the class of boundaries already introduced by Park and Paranjape [15] but also for other boundaries for which no explicit analytical results have previously been available.
21
302
314
First passage time; Varying Boundary; DIffusion process
RICCIARDI L.M.; L. SACERDOTE; SATO S.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2318/110079
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 42
  • ???jsp.display-item.citation.isi??? ND
social impact