Σεμινάριο Τομέα. Ομιλητής : Κωνσταντίνος Δαρειώτης. Παρασκευή 28/04/2023 – 13:05

Ομιλητής : Κωνσταντίνος Δαρειώτης (School of Mathematics, U. Leeds, https://eps.leeds.ac.uk/maths/staff/6172/dr-konstantinos-dareiotis)

Μέρος, ώρα : Παρασκευή 28/4, στις 13:05 στην αίθουσα Σεμιναρίων του Τομέα Μαθηματικών ΣΕΜΦΕ, κτ. Ε΄, 2ος όροφος.

ΤίτλοςRegularisation of differential equations by multiplicative fractional noises.

Περίληψη : “In this talk, we consider differential equations perturbed by multiplicative fractional Brownian noise. Depending on the value of the Hurst parameter $H$, the resulting equation is pathwise viewed as an ordinary ($H>1$), Young  ($H \in (1/2, 1)$) or rough  ($H \in (1/3, 1/2)$) differential equation. In all three regimes we show regularisation by noise phenomena by proving the strongest kind of well-posedness for equations with irregular drifts: strong existence and path-by-path uniqueness. In the Young and smooth regime $H>1/2$ the condition on the drift coefficient is optimal in the sense that it agrees with the one known for the additive case. In the rough regime $H\in(1/3,1/2)$ we assume positive but arbitrarily small drift regularity for strong  well-posedness, while for distributional drift we obtain weak existence. This is a joint work with Máté Gerencsér.