High Quality Content by WIKIPEDIA articles! In mathematics, It?'s lemma is used in It? stochastic calculus to find the differential of a function of a particular type of stochastic process. It is named after its discoverer, Kiyoshi Ito. It is the stochastic calculus counterpart of the chain rule in ordinary calculus and is best memorized using the Taylor series expansion and retaining the second order term related to the stochastic component change. The lemma is widely employed in mathematical finance and its best known application is in the derivation of the Black-Scholes equation used to value options. Ito's Lemma is also referred to currently as the It?–Doeblin Theorem in recognition of the recently discovered work of Wolfgang Doeblin.

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