For a one-dimensional jump-diffusion process X(t), starting from x > 0, it is studied the probability distribution of the area A(x) swept out by X(t) till its first-passage time below zero. In particular, it is shown that the Laplace transform and the moments of A(x) are solutions to certain partial differential-difference equations with outer conditions. The distribution of the maximum displacement of X(t) is also studied. Finally, some explicit examples are reported, regarding diffusions with and without jum
Abundo, M.r. (2013). On the First-Passage Area of a One-Dimensional Jump-Diffusion Process. METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY, 15(1), 85-103 [10.1007/s11009-011-9223-1].
On the First-Passage Area of a One-Dimensional Jump-Diffusion Process
ABUNDO, MARIO ROSOLINO
2013-01-01
Abstract
For a one-dimensional jump-diffusion process X(t), starting from x > 0, it is studied the probability distribution of the area A(x) swept out by X(t) till its first-passage time below zero. In particular, it is shown that the Laplace transform and the moments of A(x) are solutions to certain partial differential-difference equations with outer conditions. The distribution of the maximum displacement of X(t) is also studied. Finally, some explicit examples are reported, regarding diffusions with and without jum| File | Dimensione | Formato | |
|---|---|---|---|
|
abundo11c.pdf
solo utenti autorizzati
Licenza:
Copyright dell'editore
Dimensione
633.1 kB
Formato
Adobe PDF
|
633.1 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
