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Zbl 0571.60083
Nobile, A.G.; Ricciardi, L.M.; Sacerdote, L.
A note on first-passage time and some related problems.
(English)
[J] J. Appl. Probab. 22, 346-359 (1985). ISSN 0021-9002

Let X be a linear diffusion having the infinitesimal variance $\sigma\sp 2(x)$ and drift $\mu$ (x). Given the transition density (w.r.t the Lebesgue measure) $p(t,x,x\sb 0)$ $(x\sb 0$ is the starting state) the quantity - so called probability current - $$j(t,x,x\sb 0)=\mu (x)p(t,x,x\sb 0)-\partial /\partial x(\sigma\sp 2(x)p(t,x,x\sb 0))$$ may be introduced. In the paper under review the first passage times of X are studied in terms of j.
[P.Salminen]
MSC 2000:
*60J60 Diffusion processes

Keywords: Kolmogorov forward equation; probability current; first passage times

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