Smoothness of Flow and Path-by-Path Uniqueness in Stochastic Differential Equations

Siva Athreya, Suprio Bhar, Atul Shekhar

We consider the stochastic differential equation $$X_t=x_0+{\int }_0^{t}f(X_s)ds+{\int }_0^t\sigma (X_s)d{B}_s^H,$$ with $x_0\in {\mathbb{R}}^d$, $d\ge 1$, $f: \mathbb{R}^d \rightarrow…