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A note on asymptotic properties of the estimator derived from the Euler method for diffusion processes at discrete times

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  • Shoji, Isao

Abstract

In this note we investigate asymptotic properties of an estimator, called the Euler estimator, which is obtained by maximizing the likelihood function of the process discretized by the Euler method. By linking the Euler estimator of the coefficients of the drift function of a stochastic differential equation with the least square estimator and the maximum likelihood estimator based on the likelihood ratio approach, it is shown that the three estimators are equivalent. Furthermore, it is also shown that the Euler estimator of a coefficient of the diffusion term has consistency.

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  • Shoji, Isao, 1997. "A note on asymptotic properties of the estimator derived from the Euler method for diffusion processes at discrete times," Statistics & Probability Letters, Elsevier, vol. 36(2), pages 153-159, December.
    • Handle: RePEc:eee:stapro:v:36:y:1997:i:2:p:153-159
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    References listed on IDEAS

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    1. Yoshida, Nakahiro, 1992. "Estimation for diffusion processes from discrete observation," Journal of Multivariate Analysis, Elsevier, vol. 41(2), pages 220-242, May.
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    1. Wu, Shujin & Han, Dong, 2007. "Algorithmic analysis of Euler scheme for a class of stochastic differential equations with jumps," Statistics & Probability Letters, Elsevier, vol. 77(2), pages 211-219, January.
    2. Bishwal Jaya P. N., 2009. "Berry–Esseen inequalities for discretely observed diffusions," Monte Carlo Methods and Applications, De Gruyter, vol. 15(3), pages 229-239, January.
    3. Beatris Adriana Escobedo-Trujillo & José Daniel López-Barrientos & Carmen Geraldi Higuera-Chan & Francisco Alejandro Alaffita-Hernández, 2023. "Robust Statistic Estimation in Constrained Optimal Control Problems of Pollution Accumulation (Part II: Markovian Switchings)," Mathematics, MDPI, vol. 11(4), pages 1-22, February.
    4. Beatris Adriana Escobedo-Trujillo & José Daniel López-Barrientos & Carmen Geraldi Higuera-Chan & Francisco Alejandro Alaffita-Hernández, 2023. "Robust Statistic Estimation of Constrained Optimal Control Problems of Pollution Accumulation (Part I)," Mathematics, MDPI, vol. 11(4), pages 1-19, February.

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