What are stochastic processes?

A stochastic process is like a story that changes randomly over time, just like how your mood can change from happy to sad without warning.

Imagine you have a bag full of different colored marbles, red, blue, and green. Every minute, you pick one marble out of the bag at random and note down its color. This is like watching a stochastic process in action: each time you pick a marble, it's a new part of the story, and you never know what color will come next.

Think of a stochastic process as riding a roller coaster where you can't see the track ahead. Sometimes you go up high, sometimes you drop down low, all by chance. You might feel excited one moment and scared the next, just like how things change randomly in a stochastic process.

If you keep picking marbles for an hour or even a whole day, you’ll start to see patterns, maybe red appears more often than blue, but each pick is still totally random. That’s what makes it so interesting!