Strong error analysis of a stochastic exponential integrator for SPDEs driven by fractional Brownian motion with H<1/2
Abstract
Fractional Brownian motion provides a useful framework for modeling random phenomena with anti-persistent temporal correlations that arise in applications such as anomalous diffusion, hydrology, finance, and geophysical processes. In this paper, we study a class of semilinear stochastic partial differential equations driven by additive fractional Brownian motion with Hurst parameter H∈(0,1/2). We establish the well-posedness and space-time regularity of the mild solution and investigate the strong convergence of a stochastic exponential integrator for the temporal discretization. The analysis allows the linear operator to be non-self-adjoint and combines analytic semigroup estimates with the canonical Hilbert-space structure associated with fractional Brownian motion and Malliavin calculus to handle the low temporal regularity of the noise. We derive an H-dependent strong temporal convergence rate, which reaches H+1/2 under maximal spatial regularity. Numerical experiments for a stochastic advection--diffusion--reaction problem with heterogeneous Darcy flow confirm the theoretical temporal convergence rates. We also estimate the mean of the solution with different Hurst parameters H∈(0,1/2) using the Monte Carlo method.
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BibTeX
@misc{tambue2026strong,
title = {{Strong error analysis of a stochastic exponential integrator for SPDEs driven by fractional Brownian motion with H<1/2}},
author = {Antoine Tambue and Aurelien Junior Noupelah and Louis Aime Fono},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.02412},
eprint = {2610.02412},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.02412},
}
RIS
TY - UNPB
TI - Strong error analysis of a stochastic exponential integrator for SPDEs driven by fractional Brownian motion with H<1/2
AU - Antoine Tambue
AU - Aurelien Junior Noupelah
AU - Louis Aime Fono
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.02412
UR - https://arxiv.org/abs/2610.02412
AB - Fractional Brownian motion provides a useful framework for modeling random phenomena with anti-persistent temporal correlations that arise in applications such as anomalous diffusion, hydrology, finance, and geophysical processes. In this paper, we study a class of semilinear stochastic partial differential equations driven by additive fractional Brownian motion with Hurst parameter H∈(0,1/2). We establish the well-posedness and space-time regularity of the mild solution and investigate the strong convergence of a stochastic exponential integrator for the temporal discretization. The analysis allows the linear operator to be non-self-adjoint and combines analytic semigroup estimates with the canonical Hilbert-space structure associated with fractional Brownian motion and Malliavin calculus to handle the low temporal regularity of the noise. We derive an H-dependent strong temporal convergence rate, which reaches H+1/2 under maximal spatial regularity. Numerical experiments for a stochastic advection--diffusion--reaction problem with heterogeneous Darcy flow confirm the theoretical temporal convergence rates. We also estimate the mean of the solution with different Hurst parameters H∈(0,1/2) using the Monte Carlo method.
ER -