• Corpus ID: 239049617

Sharp solvability for singular SDEs

@inproceedings{Kinzebulatov2021SharpSF,
  title={Sharp solvability for singular SDEs},
  author={Damir Kinzebulatov and Yu. A. Semenov},
  year={2021}
}
Abstract. The attracting inverse-square drift provides a prototypical counterexample to solvability of singular SDEs: if the coefficient of the drift is larger than a certain critical value, then no weak solution exists. We prove a positive result on solvability of singular SDEs where this critical value is attained from below (up to strict inequality) for the entire class of form-bounded drifts. This class contains e.g. the inverse-square drift, the critical Ladyzhenskaya-Prodi-Serrin class… 

References

SHOWING 1-10 OF 23 REFERENCES
Strong solutions of stochastic equations with singular time dependent drift
Abstract.We prove existence and uniqueness of strong solutions to stochastic equations in domains with unit diffusion and singular time dependent drift b up to an explosion time. We only assume local
Stochastic ODEs and stochastic linear PDEs with critical drift: regularity, duality and uniqueness
In this paper linear stochastic transport and continuity equations with drift in critical $L^{p}$ spaces are considered. In this situation noise prevents shocks for the transport equation and
FELLER GENERATORS AND STOCHASTIC DIFFERENTIAL EQUATIONS WITH SINGULAR (FORM-BOUNDED) DRIFT
We consider the problem of constructing weak solutions to the Itô and to the Stratonovich stochastic differential equations having critical-order singularities in the drift and critical-order
Brownian motion with general drift
We construct and study the weak solution to stochastic differential equation $dX(t)=-b(X(t))dt+\sqrt{2}dW(t)$, $X_0=x$, for every $x \in \mathbb R^d$, $d \geq 3$, with $b$ in the class of weakly
A Strong Regularity Result for Parabolic Equations
We consider a parabolic equation with a drift term Δu+b∇u−ut=0. Under the condition divb=0, we prove that solutions possess dramatically better regularity than those provided by standard theory. For
Regularity theorems for parabolic equations
Abstract We study regularity properties of solutions of a parabolic equation ( ∂ t - ▿ · a · ▿ + b · ▿ + ▿ · b ^ ) u = 0 in R + × R d , d ⩾ 3 under fairly general conditions on the drift term
Singular Stochastic Differential Equations
Introduction.- 1. Stochastic Differential Equations.- 2. One-Sided Classification of Isolated Singular Points.- 3. Two-Sided Classification of Isolated Singular Points.- 4. Classification at Infinity
On the theory of the Kolmogorov operator in the spaces $L^p$ and $C_\infty$
We obtain the basic results concerning the problem of constructing operator realizations of the formal differential expression $\nabla \cdot a \cdot \nabla - b \cdot \nabla$ with measurable matrix
Stochastic Lagrangian Path for Leray’s Solutions of 3D Navier–Stokes Equations
In this paper we show the existence of stochastic Lagrangian particle trajectory for Leray's solution of 3D Navier-Stokes equations. More precisely, for any Leray's solution ${\mathbf u}$ of 3D-NSE
Brownian motion with polar drift
On cherche a approfondir la connaissance du comportement des diffusions multidimensionnelles pres des points singuliers
...
1
2
3
...