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Ito's lemma (from Taylor series) to get df

[itex] df = \frac{\partial f}{\partial x} dx + \frac{\partial f}{\partial t} dt + \frac{\partial^{2} f}{\partial x^{2}} dx^{2} + ....[/itex]

higher order terms, but they cancel out in stochastics.

but this seems to contradict the standard differential of a function from multivatiable calculus

[itex] df = \frac{\partial f}{\partial x} dx + \frac{\partial f}{\partial t} dt [/itex]

I don't get why they are different, can anyone explain?

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# Ito's lemma/taylor series vs. differential of a function

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