Student Probability/PDE Seminar: Stochastic Differential Equations with Critical Drifts

Seminar | September 15 | 2:10-3:30 p.m. | 891 Evans Hall

 Kyeongsik Nam, UC Berkeley

 Department of Mathematics

It is a classical result that SDE with additive noise whose drift term belongs to $L^q([0,T],L^p_x)$ for $\frac 2q+\frac dp< 1$ possesses a strong solution. In this talk, I will extend this result to the critical drift case. More precisely, I will construct a regular stochastic flow when drift term belongs to $L^{q,1}([0,T],L^p_x)$, which is a Lorentz space in time, for critical exponents $p$ and $q$ satisfying $\frac 2q+\frac dp=1$.