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Asymptotic properties of Monte Carlo estimators of diffusion processes

This paper studies the limit distributions of Monte Carlo estimators of diffusion processes. We examine two types of estimators based on the Euler scheme, one applied to the original processes, the other to a Doss transformation of the processes. We show that the transformation increases the speed o...

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Published in:	Journal of econometrics 2006-09, Vol.134 (1), p.1-68
Main Authors:	Detemple, Jérôme, Garcia, René, Rindisbacher, Marcel
Format:	Article
Language:	English
Subjects:	Applications Approximation Diffusion Diffusion processes Distribution theory Doss transformation Estimation Eulers equations Exact sciences and technology Insurance, economics, finance Mathematics Monte Carlo estimators Monte Carlo simulation Numerical analysis Numerical analysis. Scientific computation Numerical methods in probability and statistics Probability and statistics Sciences and techniques of general use Simulation-based estimation Statistics Studies
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description	This paper studies the limit distributions of Monte Carlo estimators of diffusion processes. We examine two types of estimators based on the Euler scheme, one applied to the original processes, the other to a Doss transformation of the processes. We show that the transformation increases the speed of convergence of the Euler scheme. We also study estimators of conditional expectations of diffusions. After characterizing expected approximation errors, we construct second-order bias-corrected estimators. We also derive new convergence results for the Mihlstein scheme. Illustrations of the results are provided in the context of simulation-based estimation of diffusion processes.
doi_str_mv	10.1016/j.jeconom.2005.06.028
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source	International Bibliography of the Social Sciences (IBSS); Backfile Package - Economics, Econometrics and Finance (Legacy) [YET]; ScienceDirect Journals; Backfile Package - Mathematics (Legacy) [YMT]
subjects	Applications Approximation Diffusion Diffusion processes Distribution theory Doss transformation Estimation Eulers equations Exact sciences and technology Insurance, economics, finance Mathematics Monte Carlo estimators Monte Carlo simulation Numerical analysis Numerical analysis. Scientific computation Numerical methods in probability and statistics Probability and statistics Sciences and techniques of general use Simulation-based estimation Statistics Studies
title	Asymptotic properties of Monte Carlo estimators of diffusion processes
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