arXiv subjects

Kerlyns Martinez

Publications and source records attributed to Kerlyns Martinez.

4 recordsLinked to original sources

arXiv2026

Expectation-Maximization algorithm to estimate the forcing parameter of a nonlinear McKean-Vlasov diffusion

In this article, we address the problem of estimating a forcing parameter in a stochastic differential equation inspired by a model that describes instantaneous turbulent kinetic energy. The stochastic differential equation we analyze is of the nonlinear McKean-Vlasov type, where the drift term depends on a power of the expected value of the solution, which also introduces nonlinearity in an algebraic sense. We propose an estimation algorithm based on the Expectation-Maximization framework and show the consistency of our method. We illustrate our findings through numerical experiments.

math.ST↗

arXiv2026

Error analysis for learning fractional stochastic differential equations with applications in neural approximations

This paper develops a framework for the error analysis in nonparametric model fitting of fractional stochastic differential equations based on discrete observations. We identify and quantify the main error sources -- time discretization, coefficient approximation, and model fitting error -- within a unified framework. Through Sobolev-type norms, we derive convergence rates that incorporate the regularity of trajectories, thereby capturing the interaction of these error components. To demonstrate the applicability of the theory, we introduce a training scheme for coefficient function estimation based on shallow neural networks and a recurrent architecture. Numerical experiments validate the theoretical findings and illustrate the effectiveness of the approach.

math.PR↗

arXiv2025

Weak rough kernel comparison via PPDEs for integrated Volterra processes

Motivated by applications in physics (e.g., turbulence intermittency) and financial mathematics (e.g., rough volatility), this paper examines a family of integrated stochastic Volterra processes characterized by a small Hurst parameter $H<\tfrac{1}{2}$. We investigate the impact of kernel approximation on the integrated process by examining the resulting weak error. Our findings quantify this error in terms of the $L^1$ norm of the difference between the two kernels, as well as the $L^1$ norm of the difference of the squares of these kernels. Our analysis is based on a path-dependent Feynman-Kac formula and the associated partial differential equation (PPDE), providing a robust and extendible framework for our analysis.

math.PR↗

arXiv2020

On the weak convergence rate of an exponential Euler scheme for SDEs governed by coefficients with superlinear growth

We consider the problem of the approximation of the solution of a one-dimensional SDE with non-globally Lipschitz drift and diffusion coefficients behaving as $x^α$, with $α>1$. We propose an (semi-explicit) exponential-Euler scheme and study its convergence through its weak approximation error. To this aim, we analyze the $C^{1,4}$ regularity of the solution of the associated backward Kolmogorov PDE using its Feynman-Kac representation and the flow derivative of the involved processes. From this, under some suitable hypotheses on the parameters of the model ensuring the control of its positive moments, we recover a rate of weak convergence of order one for the proposed exponential Euler scheme. Finally, numerical experiments are shown in order to support and complement our theoretical result.

math.PR↗