Itô calculus

Itô calculus is a branch of mathematics used to analyze systems influenced by randomness, particularly in finance and physics. It extends traditional calculus to handle stochastic processes—like stock prices—that fluctuate unpredictably over time. Unlike ordinary derivatives, Itô calculus accounts for the fact that the randomness introduces additional variability, especially when calculating how small changes accumulate. It's essential for modeling and predicting the behavior of systems with continuous, random fluctuations, providing a rigorous way to work with unpredictable data and develop strategies in uncertain environments.