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Diffusion approximation of discrete Markov chains with Binomial-like transition probabilities
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On first-hitting time of a linear boundary by perturbed brownian motion
Full text linkWe 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)
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