Itô Integral

The Itô integral is a mathematical tool used to analyze and model systems affected by random fluctuations, such as stock prices or physical processes with noise. Imagine measuring the total effect of tiny, unpredictable changes over time; the Itô integral aggregates these irregular contributions, accommodating their randomness by considering how they vary at every moment. Unlike traditional integrals, it accounts for the fact that the process is inherently unpredictable, allowing for accurate modeling of stochastic (random) systems in fields like finance, physics, and engineering.