itô's lemma

Itô's Lemma is a special way of expressing how things (like numbers or relationships between numbers) can change over time. To understand it, think of how the height of a bean sprout changes over the course of a day. You know that the sprout will get taller and taller, but how quickly or slowly that happens depends on different things, like how much water it gets and how much sunlight it gets.

Itô's Lemma is like a special formula that helps us figure out exactly how much the bean sprout will change from one day to the next. We can look at the bean sprout's starting height and the other conditions it's growing in, and the formula will tell us how tall it will be tomorrow.

Itô's Lemma is a mathematical tool that helps us track how things change over time. It can also be used to track stock prices and understand how investments can change in value. So whenever things change over time, Itô's Lemma can help us figure out exactly how quickly (or slowly) those changes will happen.