##  [Itô Integral](/ito-integral) 

  ##  [Itô Integral](https://natural.quantumdictionary.io/ito-integral-0) 

  

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**Natural & Formal Sciences Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A stochastic integral defined for adapted, square-integrable processes with respect to a semimartingale (commonly Brownian motion), constructed as the mean-square limit of nonanticipative Riemann sums using left-endpoint sampling; it satisfies an isometry relating second moments to the predictable quadratic variation of the integrator.