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math.PR2026
Itô perspective on variance renormalisation
Konstantinos Dareiotis, Máté Gerencsér
We show that the Itô solutions of the nonlinear stochastic heat equation $$ \partial_t u^\varepsilon- Îu^\varepsilon =\varepsilon^{3/4} g (u^\varepsilon) \nabla ξ_\varepsilon, $…
math.PR2025
Uniform pathwise stability of additive singular SDEs driven by fractional Brownian motion
Konstantinos Dareiotis, El Mehdi Haress, Khoa Lê
We study the long-time behaviour of solutions to a class of -dimensional stochastic differential equations driven by fractional Brownian motion with Hurst parameter $H \in (0,1)…
math.PR2024
Regularisation by Gaussian rough path lifts of fractional Brownian motions
Konstantinos Dareiotis, Máté Gerencsér, Khoa Lê +1
The aim of the paper is to show the probabilistically strong well-posedness of rough differential equations with distributional drifts driven by the Gaussian rough path lift of fra…