SDEs with critical time dependent drifts: weak solutions

Abstract

We prove the unique weak solvability of time-inhomogeneous stochastic differential equations with additive noises and drifts in critical Lebsgue space $L^q([0,T];L^p({\mathbb{R}}^d))$ with $d/p+2/q=1$. The weak uniqueness is obtained by solving corresponding Kolmogorov's backward equations in some second order Sobolev spaces, which is analytically interesting in itself.

arXiv comment29 pages

References in corpus (12)

• Pathwise uniqueness and continuous dependence for SDEs with nonregular drift
• Sobolev differentiable stochastic flows for SDEs with singular coefficients: Applications to the transport equation
• Stochastic Lagrangian path for Leray solutions of 3D Navier-Stokes equations
• SDEs with critical time dependent drifts: strong solutions
• Regular Flows for Diffusions with Rough Drifts
• On stochastic equations with drift in $L_d$
• Stochastic Lagrangian Flows for SDEs with rough coefficients
• On time inhomogeneous stochastic Itô equations with drift in $L_{d+1}$
• Existence, uniqueness and ergodic properties for time-homogeneous Itô-SDEs with locally integrable drifts and Sobolev diffusion coefficients
• On weak solutions of stochastic differential equations with sharp drift coefficients
• On strong solutions of Itô's equations with a$\in W_d^1$ and b$\in L_d$
• On stochastic Itô processes with drift in $L_d$

Cited by in corpus (2)

• SDEs with critical time dependent drifts: strong solutions
• On diffusion processes with drift in a Morrey class containing $L_{d+2}$