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Unbounded rough drivers

- I. Bailleul, M. Gubinelli
- Mathematics
- 9 January 2015

We propose a theory of linear differential equations driven by unbounded operator-valued rough signals. As an application we consider rough linear transport equations and more general linear… Expand

Flows driven by rough paths

- I. Bailleul
- Mathematics
- 5 March 2012

We devise in this work a simple mechanism for constructing flows on a Banach space from approximate flows, and show how it can be used in a simple way to reprove from scratch and extend the main… Expand

Mean field rough differential equations

- I. Bailleul, R. Catellier, F. Delarue
- Computer Science, Mathematics
- 16 February 2018

TLDR

Quasilinear generalized parabolic Anderson model equation

- I. Bailleul, A. Debussche, M. Hofmanová
- MathematicsStochastics and Partial Differential Equations…
- 21 October 2016

We present in this note a local in time well-posedness result for the singular 2-dimensional quasilinear generalized parabolic Anderson model equation $$\begin{aligned} \partial _t u - a(u)\Delta u =… Expand

Where does randomness lead in spacetime

- I. Bailleul, A. Raugi
- Mathematics
- 1 February 2010

We provide an alternative algebraic and geometric approach to the results of [I. Bailleul, Probab. Theory Related Fields 141 (2008) 283–329] describing the asymptotic behaviour of the relativistic… Expand

HIGH ORDER PARACONTROLLED CALCULUS

- I. Bailleul, F. Bernicot
- MathematicsForum of Mathematics, Sigma
- 22 September 2016

We develop in this work a general version of paracontrolled calculus that allows to treat analytically within this paradigm a whole class of singular partial differential equations with the same… Expand

Rough flows

- I. Bailleul, S. Riedel
- Mathematics, Computer ScienceJournal of the Mathematical Society of Japan
- 7 May 2015

TLDR

Small-time fluctuations for the bridge of a sub-Riemannian diffusion

- I. Bailleul, Laurent Mesnager, J. Norris
- MathematicsAnnales scientifiques de l'École Normale Sup…
- 13 May 2015

We consider small-time asymptotics for diffusion processes conditioned by their initial and final positions, under the assumption that the diffusivity has a sub-Riemannian structure, not necessarily… Expand

Flows driven by Banach space-valued rough paths

- I. Bailleul
- Mathematics
- 24 September 2013

We show in this note how the machinery of \(\mathcal{C}^{1}\)-approximate flows devised in the work Flows driven by rough paths, and applied there to reprove and extend most of the results on Banach… Expand

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