Well‐posedness of stochastic heat equation with distributional drift and skew stochastic heat equation

S Athreya, O Butkovsky, K Lê… - Communications on Pure …, 2024 - Wiley Online Library
We study stochastic reaction–diffusion equation∂ tut (x)= 1 2∂ xx 2 ut (x)+ b (ut (x))+ W ̇ t
(x), t> 0, x∈ D ∂ _tu_t (x)= 1 2 ∂^ 2_ xx u_t (x)+ b (u_t (x))+ ̇ W _ t (x),\quad t> 0,\, x ∈ D …

SDEs with supercritical distributional drifts

Z Hao, X Zhang - arXiv preprint arXiv:2312.11145, 2023 - arxiv.org
Let $ d\geq 2$. In this paper, we investigate the following stochastic differential equation
(SDE) in ${\mathbb R}^ d $ driven by Brownian motion $${\rm d} X_t= b (t, X_t){\rm d} t+\sqrt …

On multidimensional stable-driven stochastic differential equations with Besov drift

PÉ Chaudru de Raynal, S Menozzi - Electronic Journal of …, 2022 - projecteuclid.org
We establish well-posedness results for multidimensional non degenerate α-stable driven
SDEs with time inhomogeneous singular drifts in L r− B p, q− 1+ γ with γ< 1 and α in (1, 2] …

Weak well-posedness of energy solutions to singular SDEs with supercritical distributional drift

L Gräfner, N Perkowski - arXiv preprint arXiv:2407.09046, 2024 - arxiv.org
We study stochastic differential equations with additive noise and distributional drift on
$\mathbb {T}^ d $ or $\mathbb {R}^ d $ and $ d\geqslant 2$. We work in a scaling …

A simple construction of the dynamical Φ⁴₃ model

A Jagannath, N Perkowski - Transactions of the American Mathematical …, 2023 - ams.org
The $\Phi^ 4_3 $ equation is a singular stochastic PDE with important applications in
mathematical physics. Its solution usually requires advanced mathematical theories like …

Singular kinetic equations and applications

Z Hao, X Zhang, R Zhu, X Zhu - The Annals of Probability, 2024 - projecteuclid.org
In this paper we study singular kinetic equations on R 2 d by the paracontrolled distribution
method introduced in Gubinelli, Imkeller and Perkowski (Forum Math. Pi 3 (2015) e6–75) …

Degenerate McKean-Vlasov equations with drift in anisotropic negative Besov spaces

E Issoglio, S Pagliarani, F Russo… - arXiv preprint arXiv …, 2024 - arxiv.org
The paper is concerned with a McKean-Vlasov type SDE with drift in anisotropic Besov
spaces with negative regularity and with degenerate diffusion matrix under the weak H {\" o} …

Multidimensional stable driven McKean–Vlasov SDEs with distributional interaction kernel: a regularization by noise perspective

PEC de Raynal, JF Jabir, S Menozzi - Stochastics and Partial Differential …, 2024 - Springer
In this work, we are interested in establishing weak and strong well-posedness for McKean–
Vlasov SDEs with additive stable noise and a convolution type non-linear drift with singular …

[PDF][PDF] Smoothness of solutions of hyperbolic stochastic partial differential equations with L∞-vector fields

AM Bogso, M Dieye, O Menoukeu Pamen… - arXiv preprint arXiv …, 2022 - researchgate.net
In this paper we are interested in a quasi-linear hyperbolic stochastic differential equation
(HSPDE) when the vector field is merely bounded and measurable. Although the …

Effective diffusivities in periodic KPZ

Y Gu, T Komorowski - Probability Theory and Related Fields, 2024 - Springer
For the KPZ equation on a torus with a 1+ 1 spacetime white noise, it was shown in Dunlap
et al.(Commun Pure Appl Math, 2023, https://doi. org/10.1002/cpa. 22110) and Gu and …