Abrupt decorrelation for linear stochastic differential equations

Sergio I. López; Juan C. Pardo; Leandro P. R. Pimentel

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arXiv · 2509.16828

Abrupt decorrelation for linear stochastic differential equations

Sergio I. López·Juan C. Pardo·Leandro P. R. Pimentel

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Abstract

Understanding how a system loses memory of its initial state is a central problem in probability and statistics. In this manuscript, we introduce the notion of abrupt decorrelation, which explicitly characterises a sharp and sudden loss of correlation over time. We study this phenomenon within a class of linear stochastic differential equations (LSDEs), where explicit descriptions are available under various statistical distances. Our main focus is on the multivariate Ornstein-Uhlenbeck process, while in the one-dimensional case we extend the analysis to LSDEs with time-dependent drifts. The results highlight strong parallels with the cut-off phenomenon in Markov processes and contribute to a broader understanding of decorrelation in stochastic systems.

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Sergio I. López, Juan C. Pardo, Leandro P. R. Pimentel. 2025-09-20. Abrupt decorrelation for linear stochastic differential equations. https://arxiv.org/abs/2509.16828

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