Memorylessness: mathbbP(X_t+h in A,|,mathcalF_t) = mathbbP(X_t+h in A,|,X_t) — the future depends on the past only through the present. Holds for solutions of SDEs driven by Brownian motion (since Brownian increments are independent), which is why one-factor diffusion models admit PDE pricing (Feynman-Kac). Path-dependent payoffs (Asians, barriers) and non-Markovian SDEs (rough volatility, HJM general) lose this and require state augmentation or path-Monte Carlo.