HAL - L’archive ouverte pluridisciplinaire

Articles

• [hal-05024216] Linear Wavelet-Based Estimators of Partial Derivatives of Multivariate Density Function for Stationary and Ergodic Continuous Time Processes

  14 janvier, par ano.nymous@ccsd.cnrs.fr.invalid (Sultana Didi), Sultana Didi
  In this work, we propose a wavelet-based framework for estimating the derivatives of a density function in the setting of continuous, stationary, and ergodic processes. Our primary focus is the derivation of the integrated mean square error (IMSE) over compact subsets of Rd, which provides a quantitative measure of the estimation accuracy. In addition, a uniform convergence rate and normality are established. To establish the asymptotic behavior of the proposed estimators, we adopt a martingale approach that accommodates the ergodic nature of the underlying processes. Importantly, beyond ergodicity, our analysis does not require additional assumptions regarding the data. By demonstrating that the wavelet methodology remains valid under these weaker dependence conditions, we extend earlier results originally developed in the context of independent observations.

• [hal-04702353] Full Whittle inference for weak FARIMA models

  19 décembre 2025, par ano.nymous@ccsd.cnrs.fr.invalid (Samir Ben-Hariz), Samir Ben-Hariz
  This paper investigates statistical inference for weak FARIMA models in the frequency domain. We estimate the asymptotic covariance matrix of the classical Whittle estimator to achieve full inference, thereby addressing an open question posed by Shao, X. (2010). Additionally, we introduce a fast alternative to the Whittle estimator based on a one-step procedure. This method refines an initial Whittle estimator computed on a subsample using a single Fisher scoring step. The resulting estimator retains the same asymptotic properties as the Whittle estimator computed on the full sample while significantly reducing computational time.

• [hal-05403061] Global attractor of a PDE model for the kinetics of Trichoderma fungi

  8 décembre 2025, par ano.nymous@ccsd.cnrs.fr.invalid (Asmae Hardoul), Asmae Hardoul
  Partial differential equations (PDEs) are essential tools for modeling and understanding complex natural processes, particularly in biology. This research explores the growth of the fungus Trichoderma in the complex structure of soils, focusing on the production of enzymes (cellulase) during substrate degradation. The proposed reaction-diffusion model is spatialized by taking into account the diffusion of each component. We analyze the existence and uniqueness of the solutions of the obtained PDE problems, as well as their asymptotic behavior. Our results reveal the presence of a global attractor, a fundamental feature with essential implications for the long-term behavior of the system. Numerical simulations are used to illustrate the attributes of this global attractor and provide additional information on the dynamic behavior of the system.

• [hal-05396788] A Rocq Formalization of Monomial and Graded Orders

  3 décembre 2025, par ano.nymous@ccsd.cnrs.fr.invalid (Sylvie Boldo), Sylvie Boldo
  Even if binary relations and orders are a common formalization topic, we need to formalize specific orders (namely monomial and graded) in the process of formalizing in Rocq the finite element method. This article is therefore definitions, operators, and proofs of properties about relations and orders, thus providing a comprehensive Rocq library. We especially focus on monomial orders, that are total orders compatible with the monoid operation. More than its definition and proved properties, we define several of them, among them the lexicographic and grevlex orders. For the sake of genericity, we formalize the grading of an order, a high-level operator that transforms a binary relation into another one, and we prove that grading an order preserves many of its properties, such as the monomial order property. This leads us to the definition and properties of four different graded orders, with very factorized proofs. We therefore provide a comprehensive and user-friendly library in Rocq about orders, including monomial and graded orders, that contains more than 700 lemmas.

• [hal-05396759] A Rocq Formalization of Monomial and Graded Orders

  3 décembre 2025, par ano.nymous@ccsd.cnrs.fr.invalid (Sylvie Boldo), Sylvie Boldo
  Even if binary relations and orders are a common formalization topic, we need to formalize specific orders (namely monomial and graded) in the process of formalizing in Rocq the finite element method. This article is therefore definitions, operators, and proofs of properties about relations and orders, thus providing a comprehensive Rocq library. We especially focus on monomial orders, that are total orders compatible with the monoid operation. More than its definition and proved properties, we define several of them, among them the lexicographic and grevlex orders. For the sake of genericity, we formalize the grading of an order, a high-level operator that transforms a binary relation into another one, and we prove that grading an order preserves many of its properties, such as the monomial order property. This leads us to the definition and properties of four different graded orders, with very factorized proofs. We therefore provide a comprehensive and user-friendly library in Rocq about orders, including monomial and graded orders, that contains more than 700 lemmas.

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