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<p>The present research seeks to determine the consistency of Gaussian parameter estimators for the discretely observed G-Brownian motion diffusion (GBMD) process. This methodology commences with the Euler-Maruyama discretization scheme to approximate the underlying diffusion process, from which the maximum likelihood-based estimation method is utilized to derive straightforward expressions of the parameter estimators. Subsequently, under some particular reasonable assumption and boundedness conditions, we achieve the consistency of the drift parameter estimator, proving its almost sure convergence to the real value. Additionally, the mean square convergence of the volatility estimator to its real value is subject to a meticulous test. More importantly, the paper further illustrates the practical use of the GBMD process through modeling Morocco’s real long-term interest rates (IRs), considering the asymptotic properties of the estimators and reinforced by numerical simulations. The findings offer significant insights for predicting the future dynamics of Morocco’s real IRs over the coming four years.</p>

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On Consistency Gaussian Estimators for Discretely Observed G-Brownian Motion Stochastic Process with Application to Real Long-Term Rate Dynamics

  • 期刊论文

  • 发表日期：

    2025年7月10日

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  • Youssef Mahraz,
  • Toufik Chaayra,
  • Hanae El Ouardani,
  • Zakaria El Allali

摘要

The present research seeks to determine the consistency of Gaussian parameter estimators for the discretely observed G-Brownian motion diffusion (GBMD) process. This methodology commences with the Euler-Maruyama discretization scheme to approximate the underlying diffusion process, from which the maximum likelihood-based estimation method is utilized to derive straightforward expressions of the parameter estimators. Subsequently, under some particular reasonable assumption and boundedness conditions, we achieve the consistency of the drift parameter estimator, proving its almost sure convergence to the real value. Additionally, the mean square convergence of the volatility estimator to its real value is subject to a meticulous test. More importantly, the paper further illustrates the practical use of the GBMD process through modeling Morocco’s real long-term interest rates (IRs), considering the asymptotic properties of the estimators and reinforced by numerical simulations. The findings offer significant insights for predicting the future dynamics of Morocco’s real IRs over the coming four years.