Strict SDE Comparison for Cusp Coefficients and Counterexamples
We provide a tractable sufficient condition for strict comparison for solutions of the one-dimensional stochastic differential equation \[ d X_t^x=\sigma(X_t^x)\,d B_t, \quad X_0^x=x\in I=(\ell,r), \] for $\sigma>0$ and continuous. Our proof is based on a two-dimensional Lyapunov argument, which allows us to prove stri...