On boundary crossing probabilities for diffusion processes

  title={On boundary crossing probabilities for diffusion processes},
  author={Konstantin Borovkov and Andrew N. Downes},
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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Publications referenced by this paper.

The first-passage density of the Brownian motion process to a curved boundary

  • J. Durbin, D. Williams
  • J. Appl. Probab. 29,
  • 1992
Highly Influential
4 Excerpts

The first-passage density of a continuous Gaussian process to a general boundary

  • J. Durbin
  • J. Appl. Probab. 22,
  • 1985
Highly Influential
4 Excerpts

Handbook of Brownian Motion - Facts and Formulae, 2nd ed

  • A. N. Borodin, P. Salminen
  • Birkhauser Verlag, Basel,
  • 2002
2 Excerpts

Approximating the first crossing-time density for a curved boundary

  • H. E. Daniels
  • Bernoulli 2,
  • 1996

Smooth transition densities for one-dimensional diffusions

  • L.C.G. Rogers
  • Bull. London Math. Soc. 17,
  • 1985

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