On boundary crossing probabilities for diffusion processes

@inproceedings{Borovkov2010OnBC,
  title={On boundary crossing probabilities for diffusion processes},
  author={Konstantin Borovkov and Andrew N. Downes},
  year={2010}
}
In this paper we establish a relationship between the asymptotic form of conditional boundary crossing probabilities and first passage time densities for diffusion processes. We show that, under the assumption that the conditional probability that our diffusion (Xs, s ≥ 0) doesn’t cross an upper boundary g(·) prior to time t given that Xt = z behaves as (a+ o(1))(g(t)− z) as z ↑ g(t), there exists an expression for the first passage time density of g(·) at time t in terms of the coefficient a… CONTINUE READING

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