We consider the first-hitting time, \tau_ Y , of the linear boundary S(t) = a + bt by the process X_Y (t) = x + B_t +Y, with a >x, b> 0, where B_t is Brownian motion and Y is a random variable independent of B_t and such that P(x +Y a) = 1. For a given distribution function F, we find the distribution of \tau_ Y in such a way P( \tau_ Y < t) = F(t).
Abundo, M.r. (2014). On first-hitting time of a linear boundary by perturbed brownian motion. THE OPEN MATHEMATICS JOURNAL, 7, 6-8 [10.2174/1874117701407010006].
On first-hitting time of a linear boundary by perturbed brownian motion
ABUNDO, MARIO ROSOLINO
2014-01-01
Abstract
We consider the first-hitting time, \tau_ Y , of the linear boundary S(t) = a + bt by the process X_Y (t) = x + B_t +Y, with a >x, b> 0, where B_t is Brownian motion and Y is a random variable independent of B_t and such that P(x +Y a) = 1. For a given distribution function F, we find the distribution of \tau_ Y in such a way P( \tau_ Y < t) = F(t).File in questo prodotto:
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