Source: J. Appl. Probab.
Volume 48, Number 3
We propose a method for estimating first passage time densities of
one-dimensional diffusions via Monte Carlo simulation. Our approach involves a
representation of the first passage time density as the expectation of a
functional of the three-dimensional Brownian bridge. As the latter process can
be simulated exactly, our method leads to almost unbiased estimators.
Furthermore, since the density is estimated directly, a convergence of order
1 / √N, where N is the sample size, is achieved, which is
in sharp contrast to the slower nonparametric rates achieved by kernel
smoothing of cumulative distribution functions.
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