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3586Why It\^o Needs the Second DerivativeIn one paragraph, explain why It\ o's lemma has a second-derivative term even though ordinary chain rule does not.随机过程中等essay未尝试面试订阅3587Why Log GBM Loses Half Sigma SquaredWhy does d\log S t for GBM contain the drift adjustment - 2/2?随机过程中等essay未尝试面试订阅3588How Drift Cancellation Creates Local MartingalesWhat is the core idea behind turning a transformed diffusion into a local martingale by choosing the right prefactor or discount rate?随机过程中等essay未尝试面试订阅3589Why Time-Dependent Prefactors Are UsefulWhy are time-dependent factors like e -at or (1+t) -1 so common in It\ o calculations?随机过程中等essay未尝试面试订阅3590It\^o Versus Ordinary Chain RuleGive a short explanation of how It\ o's lemma should be viewed as a stochastic version of Taylor expansion rather than as a minor tweak to ordinary chain rule.随机过程中等essay未尝试面试订阅