Itô's lemma
In mathematics, Itô's lemma is an identity used in Itô calculus to find the differential of a time-dependent function of a stochastic process. It serves as the stochastic calculus counterpart of the chain rule. It can be heuristically derived by forming the Taylor series expansion of the function up to its second derivatives and retaining terms up to first order in the time increment and second order in the Wiener process increment. The lemma is widely employed in mathematical finance, and its best known application is in the derivation of the Black–Scholes equation for option values.
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Itô's lemma
In mathematics, Itô's lemma is an identity used in Itô calculus to find the differential of a time-dependent function of a stochastic process. It serves as the stochastic calculus counterpart of the chain rule. It can be heuristically derived by forming the Taylor series expansion of the function up to its second derivatives and retaining terms up to first order in the time increment and second order in the Wiener process increment. The lemma is widely employed in mathematical finance, and its best known application is in the derivation of the Black–Scholes equation for option values.
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Das Lemma von Itō (auch Itō-Fo ...... rential- und Integralrechnung.
@de
Em matemática, o lema de Itō é ...... lizada para precificar opções.
@pt
In matematica, il lemma di Itō ...... ato geometrico, non è un'area.
@it
In mathematics, Itô's lemma is ...... theory, is due to Noboru Itô.
@en
Le lemme d'Itō, ou encore form ...... entielles stochastiques (EDS).
@fr
Формула Ито — формула замены п ...... японский математик-статистик.
@ru
伊藤の補題（いとうのほだい、Itō's/Itô's lemma）は、確率微分方程式の確率過程に関する積分を簡便に計算するための方法である。伊藤清が考案した。
@ja
在随机分析中，伊藤引理（Ito's lemma）是一条非常重要的性质。發現者為日本數學家伊藤清，他指出了对于一个随机过程的函数作微分的规则。
@zh
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Das Lemma von Itō (auch Itō-Fo ...... rential- und Integralrechnung.
@de
Em matemática, o lema de Itō é ...... lizada para precificar opções.
@pt
In matematica, il lemma di Itō ...... ato geometrico, non è un'area.
@it
In mathematics, Itô's lemma is ...... es equation for option values.
@en
Le lemme d'Itō, ou encore form ...... entielles stochastiques (EDS).
@fr
Формула Ито — формула замены п ...... японский математик-статистик.
@ru
伊藤の補題（いとうのほだい、Itō's/Itô's lemma）は、確率微分方程式の確率過程に関する積分を簡便に計算するための方法である。伊藤清が考案した。
@ja
在随机分析中，伊藤引理（Ito's lemma）是一条非常重要的性质。發現者為日本數學家伊藤清，他指出了对于一个随机过程的函数作微分的规则。
@zh
label
Itô's lemma
@en
Lema de Itō
@pt
Lemma di Itō
@it
Lemma von Itō
@de
Lemme d'Itō
@fr
Формула Ито
@ru
伊藤の補題
@ja
伊藤引理
@zh