Characterization of continuous stationary fields as generalized Ornstein-Uhlenbeck fields via multi-parameter Langevin equation and multiple Riemann-Stieltjes integration
Probability
2026-03-27 v2
Abstract
In this article, we characterize continuous stationary fields via generalized Langevin dynamics. This gives natural connections between stationary fields, stationary increment fields, self-similar fields, and generalized Langevin dynamics. Our contribution extends some recently proved similar results for stochastic processes to the case of continuous random fields. As a by-product, we introduce some new results on multiple Riemann-Stieltjes integrals.
Keywords
Cite
@article{arxiv.2511.11110,
title = {Characterization of continuous stationary fields as generalized Ornstein-Uhlenbeck fields via multi-parameter Langevin equation and multiple Riemann-Stieltjes integration},
author = {Marko Voutilainen and Pauliina Ilmonen and Lauri Viitasaari},
journal= {arXiv preprint arXiv:2511.11110},
year = {2026}
}