52 citations · 134 across the 26 of their papers we have counts for
34 papers
On the parabolic model for the harmonic oscillator II: global existence and invariant measures
Aurélien Deya, Reika Fukuizumi, Laurent Thomann
We establish an a priori bound for the dynamical parabolic model with harmonic potential. This bound yields the global well-posedness of the equation and, via the Krylov-Bo…
On the parabolic model for the harmonic oscillator: diagrams and local existence
Aurélien Deya, Reika Fukuizumi, Laurent Thomann
We prove the local wellposedness of the (renormalized) parabolic model associated with the harmonic oscillator on , that is, the equation formally written as…
On the 1d stochastic Schr{ö}dinger product
Aurélien Deya
We exhibit various restrictions about the wellposedness of the Schr{\''o}dinger product $$\cl:z \longmapsto -\imath \int\_0^t e^{\imath s {\cop \partial^2\_x}}\big( z\_s\cdot Ψ\_s\…
Renormalization of a 1d quadratic Schr{ö}dinger model with additive noise
Aurélien Deya, Reika Fukuizumi, Laurent Thomann
The study is devoted to the interpretation and wellposedness of the stochastic NLS model \begin{equation*} (\imath \partial_t-Δ)u=|u|^2+\dot{B}, \quad u_0=0,\quad \quad t\in \mathb…
Hyperbolic Anderson model 2: Strichartz estimates and Stratonovich setting
Xia Chen, Aurélien Deya, Jian Song +1
We study a wave equation in dimension with a multiplicative space-time Gaussian noise. The existence and uniqueness of the Stratonovich solution is obtained under so…
On ill-posedness of nonlinear stochastic wave equations driven by rough noise
Aurélien Deya
We highlight a fundamental ill-posedness issue for nonlinear stochastic wave equations driven by a fractional noise. Namely, if the noise becomes too rough (i.e., the sum of its Hu…