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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 \[ d X_t^x=σ(X_t^x)\,d B_t, \quad X_0^x=x\in I=(\ell,r), \] for $σ>0$ and continuous. Our proof is based on a two-dimensional Lyapunov argument, which allows us t
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