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

Marko Voutilainen; Pauliina Ilmonen; Lauri Viitasaari

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arXiv · 2511.11110

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

Marko Voutilainen·Pauliina Ilmonen·Lauri Viitasaari

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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.

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Marko Voutilainen, Pauliina Ilmonen, Lauri Viitasaari. 2025-11-14. Characterization of continuous stationary fields as generalized Ornstein-Uhlenbeck fields via multi-parameter Langevin equation and multiple Riemann-Stieltjes integration. https://arxiv.org/abs/2511.11110

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