arXiv subjects

Lisandro Fermin

Publications and source records attributed to Lisandro Fermin.

4 recordsLinked to original sources

arXiv2026

Euler Scheme for Stochastic Functional Differential Equations Driven by Fractional Brownian Motion via Fractional Calculus Techniques

We study a stochastic functional differential equation (SFDE) with memory driven by a fractional Brownian motion (fBm) with Hurst parameter H>1/2. An Euler-type numerical scheme is proposed and analyzed under suitable regularity conditions on the drift and diffusion coefficients using tools from fractional calculus. We prove the convergence of the scheme and derive the corresponding rate in terms of the discretization step. Numerical simulations illustrate the theoretical results and confirm the accuracy of the proposed method.

math.NA↗

arXiv2026

A Robbins-Monro algorithm for non-parametric estimation of NAR process with Markov-Switching: asymptotic normality

This paper is the second part of our study on the non-parametric estimation of MS-NAR processes started with [L. Fermin et al. 2017]. We consider the Nadaraya-Watson type regression function estimator for non-linear autoregressive Markov switching processes. In this context the regression function estimator is interpreted as a solution of a local weighted We have introduced, in the first work, a restoration-estimation Robbins-Monro algorithm to approximate the estimator, and we proved identifiability of model and the consistency of the non-parametric estimator. In this work, we obtain the central limit theorem for the non-parametric estimator, whether the Markov chain is observed or not. Finally, we present a detailed simulation study illustrating the performances of our estimation procedure.

stat.ME↗

arXiv2025

Adaptive estimation in regression models for weakly dependent data and explanatory variable with known density

This article is dedicated to the estimation of the regression function when the explanatory variable is a weakly dependent process whose correlation coefficient exhibits exponential decay and has a known bounded density function. The accuracy of the estimation is measured using pointwise risk. A data-driven procedure is proposed using kernel estimation with bandwidth selected via the Goldenshluger-Lepski approach. We demonstrate that the resulting estimator satisfies an oracle-type inequality and it is also shown to be adaptive over H\"older classes. Additionally, unsupervised statistical learning techniques are described and applied to calibrate the method, and some simulations are provided to illustrate the performance of the method.

math.ST↗

arXiv2025

Modeling Maximum drawdown Records with Piecewise Deterministic Markov Processe in Capital Markets

We propose to model the records of the maximum Drawdown in capital markets by means a Piecewise Deterministic Markov Process (PDMP). We derive statistical results such as the mean and variance that describes the sequence of maximum Drawdown records. In addition, we developed a simulation study and techniques for estimating the parameters governing the stochastic process, using a practical example in the capital market to illustrate the procedure.

q-fin.RM↗