Rough stochastic differential equations
We build a hybrid theory of rough stochastic analysis which seamlessly combines the
advantages of both It\^ o's stochastic and Lyons' rough differential equations. This gives a …
advantages of both It\^ o's stochastic and Lyons' rough differential equations. This gives a …
[HTML][HTML] A priori estimates for rough PDEs with application to rough conservation laws
We introduce a general weak formulation for PDEs driven by rough paths, as well as a new
strategy to prove well-posedness. Our procedure is based on a combination of fundamental …
strategy to prove well-posedness. Our procedure is based on a combination of fundamental …
Non-equilibrium large deviations and parabolic-hyperbolic PDE with irregular drift
B Fehrman, B Gess - Inventiones mathematicae, 2023 - Springer
Large deviations of conservative interacting particle systems, such as the zero range
process, about their hydrodynamic limit and their respective rate functions lead to the …
process, about their hydrodynamic limit and their respective rate functions lead to the …
Quasilinear generalized parabolic Anderson model equation
I Bailleul, A Debussche, M Hofmanova - Stochastics and Partial …, 2019 - Springer
We present in this note a local in time well-posedness result for the singular 2-dimensional
quasilinear generalized parabolic Anderson model equation ∂ _t ua (u) Δ u= g (u) ξ.∂ tu-a …
quasilinear generalized parabolic Anderson model equation ∂ _t ua (u) Δ u= g (u) ξ.∂ tu-a …
Regularization by noise for stochastic Hamilton–Jacobi equations
We study regularizing effects of nonlinear stochastic perturbations for fully nonlinear PDE.
More precisely, path-by-path L^ ∞ L∞ bounds for the second derivative of solutions to such …
More precisely, path-by-path L^ ∞ L∞ bounds for the second derivative of solutions to such …
Regularization and well-posedness by noise for ordinary and partial differential equations
B Gess - Stochastic Partial Differential Equations and Related …, 2018 - Springer
We give a brief introduction and overview of the topic of regularization and well-posedness
by noise for ordinary and partial differential equations. The article is an attempt to outline in a …
by noise for ordinary and partial differential equations. The article is an attempt to outline in a …
Pathwise solutions for fully nonlinear first-and second-order partial differential equations with multiplicative rough time dependence
PE Souganidis - Singular random dynamics, 2019 - Springer
The notes are an overview of the theory of pathwise weak solutions of two classes of scalar
fully nonlinear first-and second-order degenerate parabolic partial differential equations with …
fully nonlinear first-and second-order degenerate parabolic partial differential equations with …
Non-equilibrium large deviations and parabolic-hyperbolic PDE with irregular drift
B Fehrman, B Gess - arXiv preprint arXiv:1910.11860, 2019 - arxiv.org
Large deviations of conservative interacting particle systems, such as the zero range
process, about their hydrodynamic limit and their respective rate functions lead to the …
process, about their hydrodynamic limit and their respective rate functions lead to the …
Speed of propagation for Hamilton–Jacobi equations with multiplicative rough time dependence and convex Hamiltonians
We show that the initial value problem for Hamilton–Jacobi equations with multiplicative
rough time dependence, typically stochastic, and convex Hamiltonians satisfies finite speed …
rough time dependence, typically stochastic, and convex Hamiltonians satisfies finite speed …