In stochastic calculus and specifically for mathematical finance Ito's lemma is used for time varying processes
I need to know intuitively why the Ito Integral is stochastic?
2026-03-31 07:01:47.1774940507
The Itō Integral
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To put it in simple terms:
The integral requires a measure (i.e., $dx$ in $\mathbb{R}^n$) and the measure here is a Wiener measure - a measure w.r.t. a stochastic process.
If you approach it from the direction of defining the integral as a limit of sums then in each sum you have a random number (normally distributed and all that) multiplying the integrand.
I think a good reference to look at would be Kloeden & Platen "Numerical Solution of Stochastic Differential Equations". I found Lefebvre's "Applied Stochastic Processes" helpful too.