It is studied the first-passage time (FPT) of a time homogeneous one-dimensional diffusion, driven by the stochastic differential equation dX(t) = μ(X(t))dt + σ(X(t)) dB t, X(0) = x 0, through b + Y(t), where b > x 0 and Y(t) is a compound Poisson process with rate λ > 0 starting at 0, which is independent of the Brownian motion B t . In particular, the FPT density is investigated, generalizing a previous result, already known in the case when X(t) = μt + B t, for which the FPT density is the solution of a certain integral equation. A numerical method is shown to calculate approximately the FPT density; some examples and numerical results are also reported. © 2008 Springer Science+Business Media, LLC.
Abundo, M.r. (2010). On the First Hitting Time of a One-dimensional Diffusion and a Compound Poisson Process. METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY, 12(3), 473-490 [10.1007/s11009-008-9115-1].
On the First Hitting Time of a One-dimensional Diffusion and a Compound Poisson Process
ABUNDO, MARIO ROSOLINO
2010-01-01
Abstract
It is studied the first-passage time (FPT) of a time homogeneous one-dimensional diffusion, driven by the stochastic differential equation dX(t) = μ(X(t))dt + σ(X(t)) dB t, X(0) = x 0, through b + Y(t), where b > x 0 and Y(t) is a compound Poisson process with rate λ > 0 starting at 0, which is independent of the Brownian motion B t . In particular, the FPT density is investigated, generalizing a previous result, already known in the case when X(t) = μt + B t, for which the FPT density is the solution of a certain integral equation. A numerical method is shown to calculate approximately the FPT density; some examples and numerical results are also reported. © 2008 Springer Science+Business Media, LLC.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
