Jacquier, AntoineSpiliopoulos, KonstantinosPannier, Alexander2025-02-242025-02-24A. Jacquier, K. Spiliopoulos, A. Pannier. "On the large-time behaviour of affine Volterra processes" https://arxiv.org/abs/2204.05270.https://hdl.handle.net/2144/49862We show the existence of a stationary measure for a class of multidimensional stochastic Volterra systems of affine type. These processes are in general not Markovian, a shortcoming which hinders their large-time analysis. We circumvent this issue by lifting the system to a measure-valued stochastic PDE introduced by Cuchiero and Teichmann, whence we retrieve the Markov property. Leveraging on the associated generalised Feller property, we extend the Krylov-Bogoliubov theorem to this infinite-dimensional setting and thus establish an approach to the existence of invariant measures. We present concrete examples, including the rough Heston model from Mathematical Finance.ProbabilityArticle10.48550/arXiv.2204.052701004381