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math.PR2026
On (fake) Stationarity in Stochastic Volterra Equations with Affine Drift and Regular Kernels
Emmanuel Gnabeyeu, Gilles Pagès
We investigate the fake stationarity properties of solutions to forward Stochastic Volterra Integral Equations (SVIEs) with affine drift and long-memory (regular) kernels, both on…
math.PR2026
On Path-dependent Volterra Integral Equations: Strong Well-posedness and Stochastic Numerics
Emmanuel Gnabeyeu, Gilles Pagès
The aim of this paper is to provide a comprehensive analysis of the path-dependent Stochastic Volterra Integral Equations (SVIEs), in which both the drift and the diffusion coeffic…
math.PR2026
Fake stationary rough Heston volatility: Microstructure-inspired foundations
Emmanuel Gnabeyeu, Gilles Pagès, Mathieu Rosenbaum
This paper investigates the asymptotic behavior of suitably time-modulated Hawkes processes with heavy-tailed kernels in a nearly unstable regime. We show that, under appropriate s…