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EFFICIENT ESTIMATION OF ONE-DIMENSIONAL DIFFUSION FIRST PASSAGE TIME DENSITIES VIA MONTE CARLO SIMULATION

TOMOYUKI ICHIBA and CONSTANTINOS KARDARAS
Journal of Applied Probability
Vol. 48, No. 3 (SEPTEMBER 2011), pp. 699-712
Stable URL: http://www.jstor.org/stable/23065930
Page Count: 14
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
EFFICIENT ESTIMATION OF ONE-DIMENSIONAL DIFFUSION FIRST PASSAGE TIME DENSITIES VIA MONTE CARLO SIMULATION
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Abstract

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 $1/\sqrt{\mathrm{N}}$ , 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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