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Hard · Stochastic Calculus · Quant Trader interview question · stochastic-calculus, brownian-motion, martingale, levy-characterization, quadratic-variation
Lévy's characterization provides a powerful way to identify Brownian motion. Suppose $M_t$ is a continuous local martingale with $M_0 = 0$. According to Lévy's characterization theorem, what condition on the quadratic variation process $M, M_t$ is both necessary and sufficient for $M_t$ to be a Brownian motion?