On Boundary Crossing Probabilities for Diffusion Processes

In this paper, we establish a relationship between the asymptotic form of conditional boundary crossing probabilities and first passage time densities for diffusion processes. Namely, we show that, under broad assumptions, the first crossing time density of a general curvilinear boundary by a genera...

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Bibliographic Details
Published inarXiv.org
Main Authors Borovkov, Konstantin A, Downes, Andrew N
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 17.11.2008
Subjects
Asymptotic properties
Bridge approaches
Density
Diffusion
Representations
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Summary:In this paper, we establish a relationship between the asymptotic form of conditional boundary crossing probabilities and first passage time densities for diffusion processes. Namely, we show that, under broad assumptions, the first crossing time density of a general curvilinear boundary by a general time-homogeneous diffusion process has a product-form, the factors being the transition density of the process and the coefficient of the leading term in the asymptotic representation of the non-crossing probability of the boundary by the respective diffusion bridge (as the end-point of the bridge approaches the boundary). Using a similar technique, we also demonstrate that the boundary crossing probability is a Gateaux differentiable function of the boundary and give an explicit representation of its derivative.
ISSN:2331-8422