Comparison of classical and path-by-path solutions to SDEs

Lukas Anzeletti

We consider the Stochastic Differential Equation $X_t=X_0+{\int }_0^{t}b(s,X_s)ds+B_t$, in ${\mathbb{R}}^d$. We give an example of a drift $b$ such that there does not exist a wea…