First passage probabilities of one-dimensional diffusion processes

Abstract

This work is devoted to calculating the first passage probabilities of one-dimensional diffusion processes. For a one-dimensional diffusion process, we construct a sequence of Markov chains so that their absorption probabilities approximate the first passage probability of the given diffusion process. This method is especially useful when dealing with time-dependent boundaries.

Keywords

Boundary crossing probability / first passage probability / Markov chain / Skorokhod approximation

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Higher Education Press and Springer-Verlag Berlin Heidelberg