Characterization of continuous stationary fields as generalized Ornstein-Uhlenbeck fields via multi-parameter Langevin equation and multiple Riemann-Stieltjes integration

Fuente: arXiv
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Main Authors: Voutilainen, Marko, Ilmonen, Pauliina, Viitasaari, Lauri
Format: Preprint
Published: 2025
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author Voutilainen, Marko
Ilmonen, Pauliina
Viitasaari, Lauri
author_facet Voutilainen, Marko
Ilmonen, Pauliina
Viitasaari, Lauri
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2511_11110
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Characterization of continuous stationary fields as generalized Ornstein-Uhlenbeck fields via multi-parameter Langevin equation and multiple Riemann-Stieltjes integration
Voutilainen, Marko
Ilmonen, Pauliina
Viitasaari, Lauri
Probability
60G05, 60G60, 60G10, 60G18, 26B99
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.
title Characterization of continuous stationary fields as generalized Ornstein-Uhlenbeck fields via multi-parameter Langevin equation and multiple Riemann-Stieltjes integration
topic Probability
60G05, 60G60, 60G10, 60G18, 26B99
url https://arxiv.org/abs/2511.11110