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Novikov Condition and Martingales

Hard · Stochastic Calculus · Quant Trader interview question · stochastic-calculus, martingale, novikov-condition, brownian-motion

Consider a stochastic process defined by the stochastic exponential $ \mathcal{E}(\theta \cdot W)_t = \exp(\theta W_t - \frac{1}{2} \int_0^t \theta_s^2 ds) $, where $W_t$ is a standard Brownian motion and $ \theta_t $ is a stochastic process. Under what condition is $ \mathcal{E}(\theta \cdot W)_t $ a true martingale?