Discrete sampling of an integrated diffusion process and parameter estimation of the diffusion coefficient

Arnaud Gloter

ESAIM: Probability and Statistics (2010)

  • Volume: 4, page 205-227
  • ISSN: 1292-8100

Abstract

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Let (Xt) be a diffusion on the interval (l,r) and Δn a sequence of positive numbers tending to zero. We define Ji as the integral between iΔn and (i + 1)Δn of Xs. We give an approximation of the law of (J0,...,Jn-1) by means of a Euler scheme expansion for the process (Ji). In some special cases, an approximation by an explicit Gaussian ARMA(1,1) process is obtained. When Δn = n-1 we deduce from this expansion estimators of the diffusion coefficient of X based on (Ji). These estimators are shown to be asymptotically mixed normal as n tends to infinity.

How to cite

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Gloter, Arnaud. "Discrete sampling of an integrated diffusion process and parameter estimation of the diffusion coefficient." ESAIM: Probability and Statistics 4 (2010): 205-227. <http://eudml.org/doc/197734>.

@article{Gloter2010,
abstract = { Let (Xt) be a diffusion on the interval (l,r) and Δn a sequence of positive numbers tending to zero. We define Ji as the integral between iΔn and (i + 1)Δn of Xs. We give an approximation of the law of (J0,...,Jn-1) by means of a Euler scheme expansion for the process (Ji). In some special cases, an approximation by an explicit Gaussian ARMA(1,1) process is obtained. When Δn = n-1 we deduce from this expansion estimators of the diffusion coefficient of X based on (Ji). These estimators are shown to be asymptotically mixed normal as n tends to infinity. },
author = {Gloter, Arnaud},
journal = {ESAIM: Probability and Statistics},
keywords = {Diffusion processes; discrete time observation; hidden markov model.; diffusion processes; hidden Markov model},
language = {eng},
month = {3},
pages = {205-227},
publisher = {EDP Sciences},
title = {Discrete sampling of an integrated diffusion process and parameter estimation of the diffusion coefficient},
url = {http://eudml.org/doc/197734},
volume = {4},
year = {2010},
}

TY - JOUR
AU - Gloter, Arnaud
TI - Discrete sampling of an integrated diffusion process and parameter estimation of the diffusion coefficient
JO - ESAIM: Probability and Statistics
DA - 2010/3//
PB - EDP Sciences
VL - 4
SP - 205
EP - 227
AB - Let (Xt) be a diffusion on the interval (l,r) and Δn a sequence of positive numbers tending to zero. We define Ji as the integral between iΔn and (i + 1)Δn of Xs. We give an approximation of the law of (J0,...,Jn-1) by means of a Euler scheme expansion for the process (Ji). In some special cases, an approximation by an explicit Gaussian ARMA(1,1) process is obtained. When Δn = n-1 we deduce from this expansion estimators of the diffusion coefficient of X based on (Ji). These estimators are shown to be asymptotically mixed normal as n tends to infinity.
LA - eng
KW - Diffusion processes; discrete time observation; hidden markov model.; diffusion processes; hidden Markov model
UR - http://eudml.org/doc/197734
ER -

References

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