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position at any future time 𝑡, given all past positions up to time 𝑠<𝑡, is equal to the position at time 𝑠. 3. Localized Martingales Localized martingales are processes that are not martingales everywhere but can be stopped at a time to become martingales. Example: If 𝑋𝑡​ is a stock’s price modeled