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Efficient estimation of one-dimensional diffusion first passage time densities via Monte Carlo simulation

Ichiba, Tomoyuki and Kardaras, Constantinos (2011) Efficient estimation of one-dimensional diffusion first passage time densities via Monte Carlo simulation. Journal of Applied Probability, 48 (3). pp. 699-712. ISSN 0021-9002

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Identification Number: 10.1239/jap/1316796908

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 / √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.

Item Type: Article
Official URL: https://projecteuclid.org/info/euclid.jap
Additional Information: first passage time, Monte Carlo density estimation, one-dimensional diffusion, three-dimensional Brownian bridge, rate function
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Sets: Departments > Mathematics
Date Deposited: 30 Nov 2017 14:17
Last Modified: 30 Nov 2017 14:17
URI: http://eprints.lse.ac.uk/id/eprint/85898

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